Properties

Label 342720.cp
Number of curves 4
Conductor 342720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("342720.cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 342720.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
342720.cp1 342720cp3 [0, 0, 0, -971148, 368347408] [2] 4194304  
342720.cp2 342720cp4 [0, 0, 0, -308748, -61383152] [2] 4194304  
342720.cp3 342720cp2 [0, 0, 0, -63948, 5104528] [2, 2] 2097152  
342720.cp4 342720cp1 [0, 0, 0, 8052, 467728] [2] 1048576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 342720.cp have rank \(0\).

Modular form 342720.2.a.cp

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} + 6q^{13} + q^{17} + 4q^{19} + O(q^{20}) \)

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 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.