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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 27584.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27584.b1 | 27584bc1 | \([0, 0, 0, -4492, -115952]\) | \(-38238692409/27584\) | \(-7230980096\) | \([]\) | \(36864\) | \(0.82682\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27584.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 27584.b do not have complex multiplication.Modular form 27584.2.a.b
sage: E.q_eigenform(10)