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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 100010.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100010.b1 | 100010b1 | \([1, 0, 1, -10709, 425632]\) | \(-135803877416902729/640064000\) | \(-640064000\) | \([]\) | \(100224\) | \(0.89181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100010.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100010.b do not have complex multiplication.Modular form 100010.2.a.b
sage: E.q_eigenform(10)