Properties

Label 53040cq
Number of curves 2
Conductor 53040
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("53040.cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53040cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53040.cx1 53040cq1 [0, 1, 0, -217920, -38781900] [2] 368640 \(\Gamma_0(N)\)-optimal
53040.cx2 53040cq2 [0, 1, 0, -33600, -102114252] [2] 737280  

Rank

sage: E.rank()
 

The elliptic curves in class 53040cq have rank \(0\).

Modular form 53040.2.a.cx

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + 2q^{7} + q^{9} - q^{13} + q^{15} - q^{17} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.