Show commands for:
SageMath
sage: E = EllipticCurve("30926.a1")
sage: E.isogeny_class()
Elliptic curves in class 30926f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
30926.a5 | 30926f1 | [1, 0, 1, -1151, -30498] | [2] | 33120 | \(\Gamma_0(N)\)-optimal |
30926.a4 | 30926f2 | [1, 0, 1, -23241, -1364734] | [2] | 66240 | |
30926.a6 | 30926f3 | [1, 0, 1, 9894, 636620] | [2] | 99360 | |
30926.a3 | 30926f4 | [1, 0, 1, -78466, 6927852] | [2] | 198720 | |
30926.a2 | 30926f5 | [1, 0, 1, -376681, 89208684] | [2] | 298080 | |
30926.a1 | 30926f6 | [1, 0, 1, -6031721, 5701270380] | [2] | 596160 |
Rank
sage: E.rank()
The elliptic curves in class 30926f have rank \(1\).
Modular form 30926.2.a.a
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.