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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 450800bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.bc1 | 450800bc1 | \([0, 1, 0, 32667, 2434963]\) | \(9834496/12167\) | \(-4769464000000000\) | \([]\) | \(2246400\) | \(1.6945\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450800bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 450800bc do not have complex multiplication.Modular form 450800.2.a.bc
sage: E.q_eigenform(10)