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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 19404e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19404.v1 | 19404e1 | \([0, 0, 0, -157437, 24050817]\) | \(-33958656/11\) | \(-139793288198256\) | \([]\) | \(80640\) | \(1.6885\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19404e do not have complex multiplication.Modular form 19404.2.a.e
sage: E.q_eigenform(10)