Show commands for:
SageMath
sage: E = EllipticCurve("31680.cc1")
sage: E.isogeny_class()
Elliptic curves in class 31680.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 31680.cc1 | 31680bo4 | [0, 0, 0, -255612, 49741616] | [2] | 165888 | |
| 31680.cc2 | 31680bo3 | [0, 0, 0, -16032, 771464] | [2] | 82944 | |
| 31680.cc3 | 31680bo2 | [0, 0, 0, -3612, 47216] | [2] | 55296 | |
| 31680.cc4 | 31680bo1 | [0, 0, 0, -1632, -24856] | [2] | 27648 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 31680.cc have rank \(1\).
Modular form 31680.2.a.cc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
