Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 19404b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19404.k1 | 19404b1 | \([0, 0, 0, -17493, -890771]\) | \(-33958656/11\) | \(-191760340464\) | \([]\) | \(26880\) | \(1.1391\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19404b do not have complex multiplication.Modular form 19404.2.a.b
sage: E.q_eigenform(10)