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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 37440cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.ft4 | 37440cj1 | \([0, 0, 0, -82632, 7707944]\) | \(83587439220736/13990184325\) | \(10443616637875200\) | \([2]\) | \(196608\) | \(1.7948\) | \(\Gamma_0(N)\)-optimal |
| 37440.ft2 | 37440cj2 | \([0, 0, 0, -1263612, 546707216]\) | \(18681746265374416/693005625\) | \(8277214832640000\) | \([2, 2]\) | \(393216\) | \(2.1414\) | |
| 37440.ft3 | 37440cj3 | \([0, 0, 0, -1205292, 599451824]\) | \(-4053153720264484/903687890625\) | \(-43174361318400000000\) | \([2]\) | \(786432\) | \(2.4880\) | |
| 37440.ft1 | 37440cj4 | \([0, 0, 0, -20217612, 34989916016]\) | \(19129597231400697604/26325\) | \(1257696460800\) | \([2]\) | \(786432\) | \(2.4880\) |
Rank
sage: E.rank()
The elliptic curves in class 37440cj have rank \(1\).
Complex multiplication
The elliptic curves in class 37440cj do not have complex multiplication.Modular form 37440.2.a.cj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
