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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 194271.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
194271.z1 | 194271y1 | \([1, 0, 1, -18, -288125]\) | \(-1/60291\) | \(-35862492846411\) | \([]\) | \(362880\) | \(1.2798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 194271.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 194271.z do not have complex multiplication.Modular form 194271.2.a.z
sage: E.q_eigenform(10)