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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 27584.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27584.z1 | 27584j1 | \([0, 1, 0, -129, 8159]\) | \(-912673/110336\) | \(-28923920384\) | \([]\) | \(24576\) | \(0.68679\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27584.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 27584.z do not have complex multiplication.Modular form 27584.2.a.z
sage: E.q_eigenform(10)