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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 139650.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.z1 | 139650jo1 | \([1, 1, 0, -3033125, -2034481875]\) | \(-82258857972188401/59836320\) | \(-2244796942500000\) | \([]\) | \(2592000\) | \(2.2569\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139650.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 139650.z do not have complex multiplication.Modular form 139650.2.a.z
sage: E.q_eigenform(10)