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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 139650.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.bc1 | 139650hu1 | \([1, 1, 0, -45212325, 117040222125]\) | \(-44481146267173013/20356316064\) | \(-4677539509010812500000\) | \([]\) | \(13977600\) | \(3.1152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139650.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 139650.bc do not have complex multiplication.Modular form 139650.2.a.bc
sage: E.q_eigenform(10)