Properties

Label 287490.dl
Number of curves 8
Conductor 287490
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("287490.dl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 287490.dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.dl1 287490dl8 [1, 0, 0, -480837321, -4058351458599] [2] 55738368  
287490.dl2 287490dl6 [1, 0, 0, -30053001, -63410657895] [2, 2] 27869184  
287490.dl3 287490dl7 [1, 0, 0, -27862601, -73045351335] [2] 55738368  
287490.dl4 287490dl5 [1, 0, 0, -5965446, -5509954224] [2] 18579456  
287490.dl5 287490dl3 [1, 0, 0, -2015881, -837413479] [2] 13934592  
287490.dl6 287490dl2 [1, 0, 0, -790626, 141984180] [2, 2] 9289728  
287490.dl7 287490dl1 [1, 0, 0, -681106, 216216836] [2] 4644864 \(\Gamma_0(N)\)-optimal
287490.dl8 287490dl4 [1, 0, 0, 2631874, 1043470680] [2] 18579456  

Rank

sage: E.rank()
 

The elliptic curves in class 287490.dl have rank \(0\).

Modular form 287490.2.a.dl

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.