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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 205350.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.b1 | 205350dt1 | \([1, 1, 0, -4135, -97355]\) | \(166942705/12288\) | \(575742259200\) | \([]\) | \(331776\) | \(1.0026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 205350.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 205350.b do not have complex multiplication.Modular form 205350.2.a.b
sage: E.q_eigenform(10)