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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 4400z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.g1 | 4400z1 | \([0, 1, 0, -82208, 9049588]\) | \(-38401771585/22528\) | \(-36044800000000\) | \([]\) | \(15840\) | \(1.5463\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4400z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4400z do not have complex multiplication.Modular form 4400.2.a.z
sage: E.q_eigenform(10)