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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 363726.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363726.z1 | 363726z1 | \([1, -1, 0, 53091, -5136939]\) | \(187615592384231/237141728784\) | \(-20918034754307856\) | \([]\) | \(2617344\) | \(1.8176\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 363726.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 363726.z do not have complex multiplication.Modular form 363726.2.a.z
sage: E.q_eigenform(10)