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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 114996l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 114996.p4 | 114996l1 | \([0, 1, 0, 9127, -111396]\) | \(2048000/1323\) | \(-54311296625712\) | \([2]\) | \(311040\) | \(1.3244\) | \(\Gamma_0(N)\)-optimal |
| 114996.p3 | 114996l2 | \([0, 1, 0, -38788, -954700]\) | \(9826000/5103\) | \(3351782877472512\) | \([2]\) | \(622080\) | \(1.6710\) | |
| 114996.p2 | 114996l3 | \([0, 1, 0, -155153, -24276984]\) | \(-10061824000/352947\) | \(-14489047022037168\) | \([2]\) | \(933120\) | \(1.8737\) | |
| 114996.p1 | 114996l4 | \([0, 1, 0, -2502988, -1525013116]\) | \(2640279346000/3087\) | \(2027621740693248\) | \([2]\) | \(1866240\) | \(2.2203\) |
Rank
sage: E.rank()
The elliptic curves in class 114996l have rank \(0\).
Complex multiplication
The elliptic curves in class 114996l do not have complex multiplication.Modular form 114996.2.a.l
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
