Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2640.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2640.h1 | 2640q5 | \([0, -1, 0, -62160, 5985600]\) | \(6484907238722641/283593750\) | \(1161600000000\) | \([4]\) | \(6144\) | \(1.3932\) | |
| 2640.h2 | 2640q3 | \([0, -1, 0, -18800, -985920]\) | \(179415687049201/1443420\) | \(5912248320\) | \([2]\) | \(3072\) | \(1.0467\) | |
| 2640.h3 | 2640q4 | \([0, -1, 0, -4080, 84672]\) | \(1834216913521/329422500\) | \(1349314560000\) | \([2, 4]\) | \(3072\) | \(1.0467\) | |
| 2640.h4 | 2640q2 | \([0, -1, 0, -1200, -14400]\) | \(46694890801/3920400\) | \(16057958400\) | \([2, 2]\) | \(1536\) | \(0.70009\) | |
| 2640.h5 | 2640q1 | \([0, -1, 0, 80, -1088]\) | \(13651919/126720\) | \(-519045120\) | \([2]\) | \(768\) | \(0.35352\) | \(\Gamma_0(N)\)-optimal |
| 2640.h6 | 2640q6 | \([0, -1, 0, 7920, 478272]\) | \(13411719834479/32153832150\) | \(-131702096486400\) | \([4]\) | \(6144\) | \(1.3932\) |
Rank
sage: E.rank()
The elliptic curves in class 2640.h have rank \(0\).
Complex multiplication
The elliptic curves in class 2640.h do not have complex multiplication.Modular form 2640.2.a.h
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
