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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 259182.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.r1 | 259182r1 | \([1, -1, 0, -905163, 452716919]\) | \(-19438895619/9714446\) | \(-40987441727510428458\) | \([]\) | \(11404800\) | \(2.4684\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 259182.r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 259182.r do not have complex multiplication.Modular form 259182.2.a.r
sage: E.q_eigenform(10)