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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 286110.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.r1 | 286110r1 | \([1, -1, 0, -209604240, 2566765481800]\) | \(-11780292753143153/26103515625000\) | \(-2256663595077682119140625000\) | \([]\) | \(142571520\) | \(3.9373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 286110.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 286110.r do not have complex multiplication.Modular form 286110.2.a.r
sage: E.q_eigenform(10)