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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 29232.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29232.l1 | 29232bo4 | \([0, 0, 0, -4237491, 3357139826]\) | \(2818140246756887473/314406208368\) | \(938811907687514112\) | \([2]\) | \(884736\) | \(2.4772\) | |
| 29232.l2 | 29232bo2 | \([0, 0, 0, -286131, 43529330]\) | \(867622835347633/227964231936\) | \(680697549133185024\) | \([2, 2]\) | \(442368\) | \(2.1306\) | |
| 29232.l3 | 29232bo1 | \([0, 0, 0, -101811, -11950990]\) | \(39085920587953/1955659776\) | \(5839568800579584\) | \([2]\) | \(221184\) | \(1.7840\) | \(\Gamma_0(N)\)-optimal |
| 29232.l4 | 29232bo3 | \([0, 0, 0, 716109, 280659314]\) | \(13601087408654927/19267071783792\) | \(-57531168073254371328\) | \([2]\) | \(884736\) | \(2.4772\) |
Rank
sage: E.rank()
The elliptic curves in class 29232.l have rank \(0\).
Complex multiplication
The elliptic curves in class 29232.l do not have complex multiplication.Modular form 29232.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
