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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 27584p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27584.u1 | 27584p1 | \([0, 1, 0, -81, -337]\) | \(-3631696/431\) | \(-7061504\) | \([]\) | \(3584\) | \(0.049828\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27584p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 27584p do not have complex multiplication.Modular form 27584.2.a.p
sage: E.q_eigenform(10)