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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 19404u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19404.bb1 | 19404u1 | \([0, 0, 0, -204141, -39045503]\) | \(-235165059164416/28529701497\) | \(-114140260323525744\) | \([]\) | \(168960\) | \(2.0081\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19404u do not have complex multiplication.Modular form 19404.2.a.u
sage: E.q_eigenform(10)