Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1617.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1617.g1 | 1617a1 | \([1, 1, 0, -25, -62]\) | \(-765625/33\) | \(-79233\) | \([]\) | \(144\) | \(-0.29418\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1617.g1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1617.g do not have complex multiplication.Modular form 1617.2.a.g
sage: E.q_eigenform(10)