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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 189618.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.bc1 | 189618q1 | \([1, 1, 1, -1388, 19469]\) | \(-1749947265625/14648832\) | \(-2475652608\) | \([]\) | \(169344\) | \(0.62861\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 189618.bc1 has rank \(2\).
Complex multiplication
The elliptic curves in class 189618.bc do not have complex multiplication.Modular form 189618.2.a.bc
sage: E.q_eigenform(10)