Properties

Label 55470bd
Number of curves $4$
Conductor $55470$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55470.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.x3 55470bd1 [1, 1, 1, -126695, 17282957] [4] 354816 \(\Gamma_0(N)\)-optimal
55470.x2 55470bd2 [1, 1, 1, -163675, 6322085] [2, 2] 709632  
55470.x4 55470bd3 [1, 1, 1, 631395, 50527977] [2] 1419264  
55470.x1 55470bd4 [1, 1, 1, -1550425, -738640015] [2] 1419264  

Rank

sage: E.rank()
 

The elliptic curves in class 55470bd have rank \(0\).

Modular form 55470.2.a.x

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

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 Cremona 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 Cremona labels.