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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4080x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4080.q1 | 4080x1 | \([0, -1, 0, -170, -6225]\) | \(-34158804736/1045659375\) | \(-16730550000\) | \([]\) | \(4320\) | \(0.64211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4080x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4080x do not have complex multiplication.Modular form 4080.2.a.x
sage: E.q_eigenform(10)