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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 49686.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.bc1 | 49686bj1 | \([1, 0, 1, -405942, -50977496]\) | \(77086633/32928\) | \(3160096985573822112\) | \([]\) | \(898560\) | \(2.2463\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49686.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 49686.bc do not have complex multiplication.Modular form 49686.2.a.bc
sage: E.q_eigenform(10)