Properties

Label 5054c
Number of curves 6
Conductor 5054
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("5054.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5054c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5054.c5 5054c1 [1, 1, 1, -188, -2087] [2] 2376 \(\Gamma_0(N)\)-optimal
5054.c4 5054c2 [1, 1, 1, -3798, -91615] [2] 4752  
5054.c6 5054c3 [1, 1, 1, 1617, 42677] [2] 7128  
5054.c3 5054c4 [1, 1, 1, -12823, 452773] [2] 14256  
5054.c2 5054c5 [1, 1, 1, -61558, 5869939] [2] 21384  
5054.c1 5054c6 [1, 1, 1, -985718, 376273267] [2] 42768  

Rank

sage: E.rank()
 

The elliptic curves in class 5054c have rank \(0\).

Modular form 5054.2.a.c

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.