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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 54450.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54450.bc1 | 54450bi1 | \([1, -1, 0, -1595952, -775640354]\) | \(-10461203195/162\) | \(-6961722660292950\) | \([]\) | \(709632\) | \(2.1749\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54450.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 54450.bc do not have complex multiplication.Modular form 54450.2.a.bc
sage: E.q_eigenform(10)