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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 20400.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20400.cs1 | 20400bf1 | \([0, 1, 0, -5508, -160137]\) | \(-73934023936/516375\) | \(-129093750000\) | \([]\) | \(23040\) | \(0.96548\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20400.cs1 has rank \(1\).
Complex multiplication
The elliptic curves in class 20400.cs do not have complex multiplication.Modular form 20400.2.a.cs
sage: E.q_eigenform(10)