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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 39200.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39200.cs1 | 39200c1 | \([0, -1, 0, -20008, -1304988]\) | \(-19208/5\) | \(-230592040000000\) | \([]\) | \(112896\) | \(1.4730\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39200.cs1 has rank \(1\).
Complex multiplication
The elliptic curves in class 39200.cs do not have complex multiplication.Modular form 39200.2.a.cs
sage: E.q_eigenform(10)