Show commands for:
SageMath
sage: E = EllipticCurve("348480.qt1")
sage: E.isogeny_class()
Elliptic curves in class 348480qt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 348480.qt4 | 348480qt1 | [0, 0, 0, -197472, 33083336] | [2] | 3317760 | \(\Gamma_0(N)\)-optimal |
| 348480.qt3 | 348480qt2 | [0, 0, 0, -437052, -62844496] | [2] | 6635520 | |
| 348480.qt2 | 348480qt3 | [0, 0, 0, -1939872, -1026818584] | [2] | 9953280 | |
| 348480.qt1 | 348480qt4 | [0, 0, 0, -30929052, -66206090896] | [2] | 19906560 |
Rank
sage: E.rank()
The elliptic curves in class 348480qt have rank \(0\).
Modular form 348480.2.a.qt
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
