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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 19404s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19404.w1 | 19404s1 | \([0, 0, 0, -399, -3962]\) | \(-768208/297\) | \(-2715939072\) | \([]\) | \(6912\) | \(0.51957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404s1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19404s do not have complex multiplication.Modular form 19404.2.a.s
sage: E.q_eigenform(10)