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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1002.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1002.b1 | 1002b1 | \([1, 1, 0, 564, 1872]\) | \(19785968032823/12608077824\) | \(-12608077824\) | \([]\) | \(1104\) | \(0.62711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1002.b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1002.b do not have complex multiplication.Modular form 1002.2.a.b
sage: E.q_eigenform(10)