Properties

Label 2880bd
Number of curves 8
Conductor 2880
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2880.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.bc7 2880bd1 [0, 0, 0, -12, 2576] [2] 1024 \(\Gamma_0(N)\)-optimal
2880.bc6 2880bd2 [0, 0, 0, -2892, 59024] [2, 2] 2048  
2880.bc5 2880bd3 [0, 0, 0, -5772, -78064] [2, 2] 4096  
2880.bc4 2880bd4 [0, 0, 0, -46092, 3808784] [2] 4096  
2880.bc2 2880bd5 [0, 0, 0, -77772, -8343664] [2, 2] 8192  
2880.bc8 2880bd6 [0, 0, 0, 20148, -586096] [2] 8192  
2880.bc1 2880bd7 [0, 0, 0, -1244172, -534156784] [2] 16384  
2880.bc3 2880bd8 [0, 0, 0, -63372, -11528944] [2] 16384  

Rank

sage: E.rank()
 

The elliptic curves in class 2880bd have rank \(0\).

Modular form 2880.2.a.bc

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.