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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 78400.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.z1 | 78400dl1 | \([0, 0, 0, 156800, -72716000]\) | \(14155776/84035\) | \(-2530978231040000000\) | \([]\) | \(2211840\) | \(2.2132\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 78400.z do not have complex multiplication.Modular form 78400.2.a.z
sage: E.q_eigenform(10)