We know that every elliptic curve is associated with a lattice. So is the lattice of $y^2=x(x-1)(x-λ)$ just the lattice spanned by $\{0,1,λ\}$?
If yes, is there some direct explanation? (Do not compute $g_2, g_3$)
2026-03-31 07:57:13.1774943833
The lattice of $y^2=x(x-1)(x-λ)$
102 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in ALGEBRAIC-GEOMETRY
- How to see line bundle on $\mathbb P^1$ intuitively?
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- An irreducible $k$-scheme of finite type is "geometrically equidimensional".
- Global section of line bundle of degree 0
- Is there a variant of the implicit function theorem covering a branch of a curve around a singular point?
- Singular points of a curve
- Find Canonical equation of a Hyperbola
- Picard group of a fibration
- Finding a quartic with some prescribed multiplicities
Related Questions in RIEMANN-SURFACES
- Composing with a biholomorphic function does not affect the order of pole
- open-source illustrations of Riemann surfaces
- I want the pullback of a non-closed 1-form to be closed. Is that possible?
- Reference request for Riemann Roch Theorem
- Biholomorphic Riemann Surfaces can have different differential structure?
- Monodromy representations and geodesics of singular flat metrics on $\mathbb{H}$
- How to choose a branch when there are multiple branch points?
- Questions from Forster's proof regarding unbranched holomorphic proper covering map
- Is the monodromy action of the universal covering of a Riemann surface faithful?
- Riemann sheets for combined roots
Related Questions in MODULAR-FORMS
- order of zero of modular form from it's expansion at infinity
- Derivatives of modular forms of different weight
- For $1-w\bar w$ is positive definite , there exists an $n × n$ matrix $a$ with complex entries such that $(1- w\bar w)\{a\}= 1$
- Cohomological Interpretation of Modular Forms on a Modular Curve
- A few basic questions on modular forms of congruence subgroups
- Eisenstein Series, discriminant and cusp forms
- infinite triple product
- Problem on Minkowski's reduction theory of positive definite matrix
- How to prove that $\exists u_1\in P_n$ s.t $y[u_1]$ is minimal and there are finitely many $u_1=(g_1,...,g_n) \in \Bbb Z^n$ s.t $\gcd(g_1,...,g_n)=1$
- Square of the Dedekind eta function
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
No. People usually go the other way: given the elliptic curve $E_{\tau} = \mathbb{C}/(\mathbb{Z} + \mathbb{Z} \tau)$, they compute $\lambda$ as a function of $\tau$. In this guise it's called the modular lambda function $\lambda(\tau)$, and is naturally a modular function of level $2$. I would be surprised if there were any particularly natural formula for its inverse as a function of $\tau$.