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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 69575z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69575.c1 | 69575z1 | \([0, -1, 1, -55458, -5026682]\) | \(-5451776/23\) | \(-79581841796875\) | \([]\) | \(403200\) | \(1.5220\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69575z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69575z do not have complex multiplication.Modular form 69575.2.a.z
sage: E.q_eigenform(10)