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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 41070.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41070.z1 | 41070x1 | \([1, 1, 1, -39045, 5262820875]\) | \(-1369/2488320\) | \(-11965296665574782023680\) | \([]\) | \(4102560\) | \(2.9152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41070.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41070.z do not have complex multiplication.Modular form 41070.2.a.z
sage: E.q_eigenform(10)