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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 718b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
718.a1 | 718b1 | \([1, 0, 1, -5, 0]\) | \(10218313/5744\) | \(5744\) | \([]\) | \(112\) | \(-0.58855\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 718b1 has rank \(2\).
Complex multiplication
The elliptic curves in class 718b do not have complex multiplication.Modular form 718.2.a.b
sage: E.q_eigenform(10)