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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 361998.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361998.z1 | 361998z1 | \([1, -1, 0, 1748936268, 11045149068240]\) | \(76529339407951422875/51105601752662016\) | \(-395081055550568304269875740672\) | \([]\) | \(378892800\) | \(4.3678\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 361998.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 361998.z do not have complex multiplication.Modular form 361998.2.a.z
sage: E.q_eigenform(10)