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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 272734.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272734.x1 | 272734x1 | \([1, -1, 0, 13711, 174257]\) | \(165483351/103684\) | \(-178595587249156\) | \([]\) | \(866304\) | \(1.4237\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 272734.x1 has rank \(2\).
Complex multiplication
The elliptic curves in class 272734.x do not have complex multiplication.Modular form 272734.2.a.x
sage: E.q_eigenform(10)