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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 54390.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54390.bc1 | 54390bh1 | \([1, 0, 1, -2623, 50978]\) | \(40708441207609/449550000\) | \(22027950000\) | \([]\) | \(57600\) | \(0.79912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54390.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 54390.bc do not have complex multiplication.Modular form 54390.2.a.bc
sage: E.q_eigenform(10)