Properties

Label 55545.c
Number of curves 4
Conductor 55545
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55545.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55545.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.c1 55545f4 [1, 1, 1, -2671990, -1682212750] [2] 1013760  
55545.c2 55545f2 [1, 1, 1, -172465, -24527770] [2, 2] 506880  
55545.c3 55545f1 [1, 1, 1, -42860, 3000332] [4] 253440 \(\Gamma_0(N)\)-optimal
55545.c4 55545f3 [1, 1, 1, 253380, -126049218] [2] 1013760  

Rank

sage: E.rank()
 

The elliptic curves in class 55545.c have rank \(0\).

Modular form 55545.2.a.c

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.