Properties

Label 184110.w
Number of curves $8$
Conductor $184110$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 184110.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
184110.w1 184110bc7 \([1, 0, 1, -40962678, 100905259198]\) \(161572377633716256481/914742821250\) \(43034881914131771250\) \([2]\) \(14155776\) \(2.9590\)  
184110.w2 184110bc4 \([1, 0, 1, -7855368, -8474838362]\) \(1139466686381936641/4080\) \(191947194480\) \([2]\) \(3538944\) \(2.2658\)  
184110.w3 184110bc5 \([1, 0, 1, -2606428, 1516544198]\) \(41623544884956481/2962701562500\) \(139382905147889062500\) \([2, 2]\) \(7077888\) \(2.6124\)  
184110.w4 184110bc3 \([1, 0, 1, -519848, -115995994]\) \(330240275458561/67652010000\) \(3182748411870810000\) \([2, 2]\) \(3538944\) \(2.2658\)  
184110.w5 184110bc2 \([1, 0, 1, -490968, -132446042]\) \(278202094583041/16646400\) \(783144553478400\) \([2, 2]\) \(1769472\) \(1.9192\)  
184110.w6 184110bc1 \([1, 0, 1, -28888, -2324314]\) \(-56667352321/16711680\) \(-786215708590080\) \([2]\) \(884736\) \(1.5727\) \(\Gamma_0(N)\)-optimal
184110.w7 184110bc6 \([1, 0, 1, 1104652, -695617594]\) \(3168685387909439/6278181696900\) \(-295362589008735468900\) \([2]\) \(7077888\) \(2.6124\)  
184110.w8 184110bc8 \([1, 0, 1, 2364542, 6618747806]\) \(31077313442863199/420227050781250\) \(-19769951824035644531250\) \([2]\) \(14155776\) \(2.9590\)  

Rank

sage: E.rank()
 

The elliptic curves in class 184110.w have rank \(1\).

Complex multiplication

The elliptic curves in class 184110.w do not have complex multiplication.

Modular form 184110.2.a.w

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

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.