Show commands for:
SageMath
sage: E = EllipticCurve("cl1")
sage: E.isogeny_class()
Elliptic curves in class 11760.cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
11760.cl1 | 11760co7 | [0, 1, 0, -5057600, 2752600500] | [2] | 663552 | |
11760.cl2 | 11760co4 | [0, 1, 0, -4516640, 3693127668] | [2] | 221184 | |
11760.cl3 | 11760co6 | [0, 1, 0, -2117600, -1155247500] | [2, 2] | 331776 | |
11760.cl4 | 11760co3 | [0, 1, 0, -2101920, -1173630732] | [2] | 165888 | |
11760.cl5 | 11760co2 | [0, 1, 0, -283040, 57311988] | [2, 2] | 110592 | |
11760.cl6 | 11760co5 | [0, 1, 0, -63520, 144154100] | [4] | 221184 | |
11760.cl7 | 11760co1 | [0, 1, 0, -32160, -791820] | [2] | 55296 | \(\Gamma_0(N)\)-optimal |
11760.cl8 | 11760co8 | [0, 1, 0, 571520, -3886317772] | [4] | 663552 |
Rank
sage: E.rank()
The elliptic curves in class 11760.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 11760.cl do not have complex multiplication.Modular form 11760.2.a.cl
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.