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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 455175.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 455175.q1 | 455175q1 | \([0, 0, 1, -1080910575, 13503927347606]\) | \(470357606027980800/6896562077111\) | \(2047846913093939241761623125\) | \([]\) | \(313528320\) | \(4.0439\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 455175.q1 has rank \(1\).
Complex multiplication
The elliptic curves in class 455175.q do not have complex multiplication.Modular form 455175.2.a.q
sage: E.q_eigenform(10)