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Properties

Label 5610.q
Number of curves $8$
Conductor $5610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.q1 5610t7 \([1, 0, 1, -201236483, -1098790303234]\) \(901247067798311192691198986281/552431869440\) \(552431869440\) \([2]\) \(663552\) \(2.9608\)  
5610.q2 5610t8 \([1, 0, 1, -12661763, -16927055362]\) \(224494757451893010998773801/6152490825146276160000\) \(6152490825146276160000\) \([2]\) \(663552\) \(2.9608\)  
5610.q3 5610t6 \([1, 0, 1, -12577283, -17169377794]\) \(220031146443748723000125481/172266701724057600\) \(172266701724057600\) \([2, 2]\) \(331776\) \(2.6142\)  
5610.q4 5610t4 \([1, 0, 1, -2484908, -1506795694]\) \(1696892787277117093383481/1440538624914939000\) \(1440538624914939000\) \([6]\) \(221184\) \(2.4115\)  
5610.q5 5610t5 \([1, 0, 1, -1627388, 790397138]\) \(476646772170172569823801/5862293314453125000\) \(5862293314453125000\) \([6]\) \(221184\) \(2.4115\)  
5610.q6 5610t3 \([1, 0, 1, -780803, -272099842]\) \(-52643812360427830814761/1504091705903677440\) \(-1504091705903677440\) \([2]\) \(165888\) \(2.2676\)  
5610.q7 5610t2 \([1, 0, 1, -189908, -12291694]\) \(757443433548897303481/373234243041000000\) \(373234243041000000\) \([2, 6]\) \(110592\) \(2.0649\)  
5610.q8 5610t1 \([1, 0, 1, 43372, -1467502]\) \(9023321954633914439/6156756739584000\) \(-6156756739584000\) \([6]\) \(55296\) \(1.7183\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 5610.q do not have complex multiplication.

Modular form 5610.2.a.q

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.