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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 100005b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100005.b1 | 100005b1 | \([0, 1, 1, -1651, -26354]\) | \(497998408351744/562528125\) | \(562528125\) | \([]\) | \(58320\) | \(0.59269\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100005b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 100005b do not have complex multiplication.Modular form 100005.2.a.b
sage: E.q_eigenform(10)