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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 106722.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.z1 | 106722bc1 | \([1, -1, 0, 172947, -6701689]\) | \(3267/2\) | \(-350221061297137338\) | \([]\) | \(1571328\) | \(2.0556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 106722.z do not have complex multiplication.Modular form 106722.2.a.z
sage: E.q_eigenform(10)