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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 27584r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27584.j1 | 27584r1 | \([0, -1, 0, -25, 89]\) | \(-438976/431\) | \(-1765376\) | \([]\) | \(3072\) | \(-0.10542\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27584r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 27584r do not have complex multiplication.Modular form 27584.2.a.r
sage: E.q_eigenform(10)