Show commands:
SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 134640.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134640.fj1 | 134640bl1 | \([0, 0, 0, -412347, -123896086]\) | \(-2596717791529849/718080000000\) | \(-2144175390720000000\) | \([]\) | \(2709504\) | \(2.2332\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 134640.fj1 has rank \(0\).
Complex multiplication
The elliptic curves in class 134640.fj do not have complex multiplication.Modular form 134640.2.a.fj
sage: E.q_eigenform(10)