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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 286650r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.r1 | 286650r1 | \([1, -1, 0, -1655082, -729633164]\) | \(4772330903305/570306048\) | \(59918348461754764800\) | \([]\) | \(12337920\) | \(2.5259\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 286650r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 286650r do not have complex multiplication.Modular form 286650.2.a.r
sage: E.q_eigenform(10)