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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 86190.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86190.p1 | 86190o1 | \([1, 1, 0, -17072, -11121144]\) | \(-674636521/65025000\) | \(-53042890133025000\) | \([]\) | \(823680\) | \(1.8887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 86190.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 86190.p do not have complex multiplication.Modular form 86190.2.a.p
sage: E.q_eigenform(10)