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SageMath
sage: E = EllipticCurve("1344.q1")
sage: E.isogeny_class()
Elliptic curves in class 1344.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 1344.q1 | 1344g4 | [0, 1, 0, -86017, 9681503] | [2] | 3072 | |
| 1344.q2 | 1344g5 | [0, 1, 0, -58497, -5412897] | [2] | 6144 | |
| 1344.q3 | 1344g3 | [0, 1, 0, -6657, 71775] | [2, 2] | 3072 | |
| 1344.q4 | 1344g2 | [0, 1, 0, -5377, 149855] | [2, 2] | 1536 | |
| 1344.q5 | 1344g1 | [0, 1, 0, -257, 3423] | [2] | 768 | \(\Gamma_0(N)\)-optimal |
| 1344.q6 | 1344g6 | [0, 1, 0, 24703, 579807] | [4] | 6144 |
Rank
sage: E.rank()
The elliptic curves in class 1344.q have rank \(0\).
Modular form 1344.2.a.q
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
