Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 41650c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41650.x1 | 41650c1 | \([1, 0, 1, -117281526, -488938194552]\) | \(-1980652037510828689/278528000000\) | \(-25088413952000000000000\) | \([]\) | \(5806080\) | \(3.3146\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 41650c do not have complex multiplication.Modular form 41650.2.a.c
sage: E.q_eigenform(10)