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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 5175.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5175.z1 | 5175t1 | \([0, 0, 1, -165, -819]\) | \(-5451776/23\) | \(-2095875\) | \([]\) | \(1344\) | \(0.067596\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5175.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5175.z do not have complex multiplication.Modular form 5175.2.a.z
sage: E.q_eigenform(10)