Properties

Label 2880.y
Number of curves 8
Conductor 2880
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2880.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.y1 2880r7 [0, 0, 0, -1244172, 534156784] [2] 16384  
2880.y2 2880r5 [0, 0, 0, -77772, 8343664] [2, 2] 8192  
2880.y3 2880r8 [0, 0, 0, -63372, 11528944] [2] 16384  
2880.y4 2880r3 [0, 0, 0, -46092, -3808784] [2] 4096  
2880.y5 2880r4 [0, 0, 0, -5772, 78064] [2, 2] 4096  
2880.y6 2880r2 [0, 0, 0, -2892, -59024] [2, 2] 2048  
2880.y7 2880r1 [0, 0, 0, -12, -2576] [2] 1024 \(\Gamma_0(N)\)-optimal
2880.y8 2880r6 [0, 0, 0, 20148, 586096] [2] 8192  

Rank

sage: E.rank()
 

The elliptic curves in class 2880.y have rank \(1\).

Modular form 2880.2.a.y

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.