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SageMath
sage: E = EllipticCurve("4032.m1")
sage: E.isogeny_class()
Elliptic curves in class 4032.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 4032.m1 | 4032bl4 | [0, 0, 0, -774156, 262174736] | [2] | 24576 | |
| 4032.m2 | 4032bl5 | [0, 0, 0, -526476, -145621744] | [2] | 49152 | |
| 4032.m3 | 4032bl3 | [0, 0, 0, -59916, 1997840] | [2, 2] | 24576 | |
| 4032.m4 | 4032bl2 | [0, 0, 0, -48396, 4094480] | [2, 2] | 12288 | |
| 4032.m5 | 4032bl1 | [0, 0, 0, -2316, 94736] | [2] | 6144 | \(\Gamma_0(N)\)-optimal |
| 4032.m6 | 4032bl6 | [0, 0, 0, 222324, 15432464] | [2] | 49152 |
Rank
sage: E.rank()
The elliptic curves in class 4032.m have rank \(0\).
Modular form 4032.2.a.m
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.
