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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 51301b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51301.b1 | 51301b1 | \([1, 1, 0, -1699, 27774]\) | \(-912673/61\) | \(-36284222581\) | \([]\) | \(48384\) | \(0.77819\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51301b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51301b do not have complex multiplication.Modular form 51301.2.a.b
sage: E.q_eigenform(10)