Show commands:
SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 425880.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 425880.cr1 | 425880cr1 | \([0, 0, 0, -35616243, -85853017042]\) | \(-693346671296498/40610171875\) | \(-292652623704665952000000\) | \([]\) | \(62899200\) | \(3.2588\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 425880.cr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 425880.cr do not have complex multiplication.Modular form 425880.2.a.cr
sage: E.q_eigenform(10)