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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 55473p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55473.g1 | 55473p1 | \([0, 1, 1, -19051, 1010452]\) | \(-270622818304/1449459\) | \(-4095824713299\) | \([]\) | \(141120\) | \(1.2646\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55473p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 55473p do not have complex multiplication.Modular form 55473.2.a.p
sage: E.q_eigenform(10)