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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 78400.ex
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.ex1 | 78400ke1 | \([0, 0, 0, -24500, 1715000]\) | \(-34560/7\) | \(-329417200000000\) | \([]\) | \(276480\) | \(1.5082\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.ex1 has rank \(0\).
Complex multiplication
The elliptic curves in class 78400.ex do not have complex multiplication.Modular form 78400.2.a.ex
sage: E.q_eigenform(10)