Properties

Label 5610t
Number of curves 8
Conductor 5610
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("5610.q1")
sage: E.isogeny_class()

Elliptic curves in class 5610t

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
5610.q8 5610t1 [1, 0, 1, 43372, -1467502] 6 55296 \(\Gamma_0(N)\)-optimal
5610.q7 5610t2 [1, 0, 1, -189908, -12291694] 12 110592  
5610.q6 5610t3 [1, 0, 1, -780803, -272099842] 2 165888  
5610.q4 5610t4 [1, 0, 1, -2484908, -1506795694] 6 221184  
5610.q5 5610t5 [1, 0, 1, -1627388, 790397138] 6 221184  
5610.q3 5610t6 [1, 0, 1, -12577283, -17169377794] 4 331776  
5610.q1 5610t7 [1, 0, 1, -201236483, -1098790303234] 2 663552  
5610.q2 5610t8 [1, 0, 1, -12661763, -16927055362] 2 663552  

Rank

sage: E.rank()

The elliptic curves in class 5610t have rank \(0\).

Modular form 5610.2.a.q

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 2q^{13} + 4q^{14} + q^{15} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.