Show commands:
SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 41650bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41650.d1 | 41650bf1 | \([1, 0, 1, -1681951, -945594702]\) | \(-953790341/147968\) | \(-81635346961000000000\) | \([]\) | \(2056320\) | \(2.5495\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650bf1 has rank \(0\).
Complex multiplication
The elliptic curves in class 41650bf do not have complex multiplication.Modular form 41650.2.a.bf
sage: E.q_eigenform(10)