Show commands for:
SageMath
sage: E = EllipticCurve("97020.cu1")
sage: E.isogeny_class()
Elliptic curves in class 97020.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 97020.cu1 | 97020cv4 | [0, 0, 0, -3131247, -2132671786] | [2] | 1492992 | |
| 97020.cu2 | 97020cv3 | [0, 0, 0, -196392, -33076519] | [2] | 746496 | |
| 97020.cu3 | 97020cv2 | [0, 0, 0, -44247, -2024386] | [2] | 497664 | |
| 97020.cu4 | 97020cv1 | [0, 0, 0, -19992, 1065701] | [2] | 248832 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.cu have rank \(0\).
Modular form 97020.2.a.cu
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.
