Properties

Label 223440ct
Number of curves $4$
Conductor $223440$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("223440.fd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 223440ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
223440.fd4 223440ct1 [0, 1, 0, -7856, 454740] [2] 663552 \(\Gamma_0(N)\)-optimal
223440.fd3 223440ct2 [0, 1, 0, -148976, 22074324] [2, 2] 1327104  
223440.fd1 223440ct3 [0, 1, 0, -2383376, 1415446164] [2] 2654208  
223440.fd2 223440ct4 [0, 1, 0, -172496, 14613780] [2] 2654208  

Rank

sage: E.rank()
 

The elliptic curves in class 223440ct have rank \(0\).

Modular form 223440.2.a.fd

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{9} + 4q^{11} + 2q^{13} - q^{15} + 2q^{17} - q^{19} + O(q^{20}) \)

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.