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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 455175.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
455175.x1 | 455175x1 | \([0, 0, 1, -105825, -13206344]\) | \(39814672384/153125\) | \(504070751953125\) | \([]\) | \(3732480\) | \(1.6795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 455175.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 455175.x do not have complex multiplication.Modular form 455175.2.a.x
sage: E.q_eigenform(10)