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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 4650.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.bc1 | 4650bf1 | \([1, 1, 1, 13862, 1186031]\) | \(150823633267/395392104\) | \(-772250203125000\) | \([]\) | \(18720\) | \(1.5404\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4650.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4650.bc do not have complex multiplication.Modular form 4650.2.a.bc
sage: E.q_eigenform(10)