Show commands:
SageMath
E = EllipticCurve("ja1")
E.isogeny_class()
Elliptic curves in class 308550.ja
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308550.ja1 | 308550ja5 | \([1, 0, 0, -1194705663, 15894130579317]\) | \(6812873765474836663297/74052\) | \(2049806799562500\) | \([2]\) | \(62914560\) | \(3.4416\) | |
| 308550.ja2 | 308550ja3 | \([1, 0, 0, -74669163, 248340710817]\) | \(1663303207415737537/5483698704\) | \(151792293121202250000\) | \([2, 2]\) | \(31457280\) | \(3.0950\) | |
| 308550.ja3 | 308550ja6 | \([1, 0, 0, -73640663, 255514498317]\) | \(-1595514095015181697/95635786040388\) | \(-2647259824273371963562500\) | \([2]\) | \(62914560\) | \(3.4416\) | |
| 308550.ja4 | 308550ja2 | \([1, 0, 0, -4731163, 3767524817]\) | \(423108074414017/23284318464\) | \(644524851600036000000\) | \([2, 2]\) | \(15728640\) | \(2.7484\) | |
| 308550.ja5 | 308550ja1 | \([1, 0, 0, -859163, -232251183]\) | \(2533811507137/625016832\) | \(17300866311168000000\) | \([2]\) | \(7864320\) | \(2.4019\) | \(\Gamma_0(N)\)-optimal |
| 308550.ja6 | 308550ja4 | \([1, 0, 0, 3254837, 15195490817]\) | \(137763859017023/3683199928848\) | \(-101953333580467058250000\) | \([2]\) | \(31457280\) | \(3.0950\) |
Rank
sage: E.rank()
The elliptic curves in class 308550.ja have rank \(1\).
Complex multiplication
The elliptic curves in class 308550.ja do not have complex multiplication.Modular form 308550.2.a.ja
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
