Show commands for:
SageMath
sage: E = EllipticCurve("15680.n1")
sage: E.isogeny_class()
Elliptic curves in class 15680.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 15680.n1 | 15680s3 | [0, 1, 0, -8101, 277899] | [2] | 17280 | |
| 15680.n2 | 15680s4 | [0, 1, 0, -7121, 348655] | [2] | 34560 | |
| 15680.n3 | 15680s1 | [0, 1, 0, -261, -1205] | [2] | 5760 | \(\Gamma_0(N)\)-optimal |
| 15680.n4 | 15680s2 | [0, 1, 0, 719, -7281] | [2] | 11520 |
Rank
sage: E.rank()
The elliptic curves in class 15680.n have rank \(0\).
Modular form 15680.2.a.n
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.
