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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 151725.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151725.j1 | 151725g1 | \([0, 1, 1, -75864908, 243666466094]\) | \(443032031678464/21012699645\) | \(2290304623501668881953125\) | \([]\) | \(31021056\) | \(3.4348\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 151725.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 151725.j do not have complex multiplication.Modular form 151725.2.a.j
sage: E.q_eigenform(10)