Properties

Label 26640.p
Number of curves $6$
Conductor $26640$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("26640.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26640.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26640.p1 26640be4 [0, 0, 0, -49104723, 132444219922] [2] 1327104  
26640.p2 26640be6 [0, 0, 0, -43650003, -110517818222] [2] 2654208  
26640.p3 26640be3 [0, 0, 0, -4222803, 375124498] [2, 2] 1327104  
26640.p4 26640be2 [0, 0, 0, -3070803, 2066951698] [2, 2] 663552  
26640.p5 26640be1 [0, 0, 0, -121683, 56241682] [2] 331776 \(\Gamma_0(N)\)-optimal
26640.p6 26640be5 [0, 0, 0, 16772397, 2991126418] [2] 2654208  

Rank

sage: E.rank()
 

The elliptic curves in class 26640.p have rank \(0\).

Modular form 26640.2.a.p

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.