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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 86190p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86190.s1 | 86190p1 | \([1, 1, 0, 8588018, -18680853836]\) | \(414491631408272360789951/1132262271188620848000\) | \(-191352323830876923312000\) | \([]\) | \(9676800\) | \(3.1510\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 86190p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 86190p do not have complex multiplication.Modular form 86190.2.a.p
sage: E.q_eigenform(10)