Properties

Label 65520.r
Number of curves 8
Conductor 65520
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("65520.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 65520.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
65520.r1 65520cq8 [0, 0, 0, -5787425523, -169463525207758] [2] 21233664  
65520.r2 65520cq6 [0, 0, 0, -361714323, -2647864079278] [2, 2] 10616832  
65520.r3 65520cq7 [0, 0, 0, -357269043, -2716116019342] [2] 21233664  
65520.r4 65520cq5 [0, 0, 0, -71482323, -232237338478] [2] 7077888  
65520.r5 65520cq3 [0, 0, 0, -22885203, -40302937582] [2] 5308416  
65520.r6 65520cq2 [0, 0, 0, -5962323, -991050478] [2, 2] 3538944  
65520.r7 65520cq1 [0, 0, 0, -3704403, 2729550098] [2] 1769472 \(\Gamma_0(N)\)-optimal
65520.r8 65520cq4 [0, 0, 0, 23430957, -7863199342] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 65520.r have rank \(0\).

Modular form 65520.2.a.r

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.