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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 19404m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19404.u1 | 19404m1 | \([0, 0, 0, -13377, -823543]\) | \(-562432/297\) | \(-139793288198256\) | \([]\) | \(64512\) | \(1.4184\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19404m do not have complex multiplication.Modular form 19404.2.a.m
sage: E.q_eigenform(10)