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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 78408.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78408.z1 | 78408o1 | \([0, 0, 0, -3267, -35937]\) | \(2304\) | \(1673742487824\) | \([]\) | \(85680\) | \(1.0417\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78408.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78408.z do not have complex multiplication.Modular form 78408.2.a.z
sage: E.q_eigenform(10)