Properties

Label 243360.cx
Number of curves $4$
Conductor $243360$
CM no
Rank $2$
Graph

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

Elliptic curves in class 243360.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
243360.cx1 243360cx2 \([0, 0, 0, -346058427, 2477068906754]\) \(2543984126301795848/909361981125\) \(1638303640357987077696000\) \([2]\) \(66060288\) \(3.6156\)  
243360.cx2 243360cx4 \([0, 0, 0, -178748427, -900920753746]\) \(350584567631475848/8259273550125\) \(14879880844746068234304000\) \([2]\) \(66060288\) \(3.6156\)  
243360.cx3 243360cx1 \([0, 0, 0, -24747177, 26813576504]\) \(7442744143086784/2927948765625\) \(659372892900519681000000\) \([2, 2]\) \(33030144\) \(3.2690\) \(\Gamma_0(N)\)-optimal
243360.cx4 243360cx3 \([0, 0, 0, 79357668, 193547896256]\) \(3834800837445824/3342041015625\) \(-48168083344329000000000000\) \([2]\) \(66060288\) \(3.6156\)  

Rank

sage: E.rank()
 

The elliptic curves in class 243360.cx have rank \(2\).

Complex multiplication

The elliptic curves in class 243360.cx do not have complex multiplication.

Modular form 243360.2.a.cx

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} - 2 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.