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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 55545.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55545.z1 | 55545w1 | \([0, 1, 1, -3429362230, 101340200258131]\) | \(-2476357085090396229632/1030161895751953125\) | \(-1855478840271399924774169921875\) | \([]\) | \(158340096\) | \(4.5161\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55545.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 55545.z do not have complex multiplication.Modular form 55545.2.a.z
sage: E.q_eigenform(10)