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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 66248r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66248.s1 | 66248r1 | \([0, 1, 0, -135256, -17823779]\) | \(12544\) | \(21815265186407056\) | \([]\) | \(322560\) | \(1.8786\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 66248r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 66248r do not have complex multiplication.Modular form 66248.2.a.r
sage: E.q_eigenform(10)