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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 66654p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66654.b1 | 66654p1 | \([1, -1, 0, -4651596, 12172558608]\) | \(-194975262337/1008189504\) | \(-57556236474579761464896\) | \([]\) | \(6782976\) | \(3.0515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 66654p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 66654p do not have complex multiplication.Modular form 66654.2.a.p
sage: E.q_eigenform(10)