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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1410.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1410.b1 | 1410a1 | \([1, 1, 0, -418773, -104507667]\) | \(-8121969458732291369689/2284200000000000\) | \(-2284200000000000\) | \([]\) | \(15840\) | \(1.9283\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1410.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1410.b do not have complex multiplication.Modular form 1410.2.a.b
sage: E.q_eigenform(10)