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SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 78400.gr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.gr1 | 78400z1 | \([0, 0, 0, -980, -13720]\) | \(-34560/7\) | \(-21082700800\) | \([]\) | \(55296\) | \(0.70345\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.gr1 has rank \(0\).
Complex multiplication
The elliptic curves in class 78400.gr do not have complex multiplication.Modular form 78400.2.a.gr
sage: E.q_eigenform(10)