Show commands:
SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 221760.fl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.fl1 | 221760de3 | \([0, 0, 0, -19002828, 31883804048]\) | \(3971101377248209009/56495958750\) | \(10796545849098240000\) | \([2]\) | \(9437184\) | \(2.7918\) | |
| 221760.fl2 | 221760de2 | \([0, 0, 0, -1221708, 468121232]\) | \(1055257664218129/115307784900\) | \(22035660850357862400\) | \([2, 2]\) | \(4718592\) | \(2.4452\) | |
| 221760.fl3 | 221760de1 | \([0, 0, 0, -288588, -51813232]\) | \(13908844989649/1980372240\) | \(378455028651786240\) | \([2]\) | \(2359296\) | \(2.0987\) | \(\Gamma_0(N)\)-optimal |
| 221760.fl4 | 221760de4 | \([0, 0, 0, 1629492, 2328244112]\) | \(2503876820718671/13702874328990\) | \(-2618660064023992074240\) | \([2]\) | \(9437184\) | \(2.7918\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.fl have rank \(1\).
Complex multiplication
The elliptic curves in class 221760.fl do not have complex multiplication.Modular form 221760.2.a.fl
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
