Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("2880.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.a8 2880n1 [0, 0, 0, 852, -29392] [2] 3072 \(\Gamma_0(N)\)-optimal
2880.a6 2880n2 [0, 0, 0, -10668, -384208] [2, 2] 6144  
2880.a7 2880n3 [0, 0, 0, -7788, 865712] [2] 9216  
2880.a4 2880n4 [0, 0, 0, -166188, -26076112] [2] 12288  
2880.a5 2880n5 [0, 0, 0, -39468, 2599472] [2] 12288  
2880.a3 2880n6 [0, 0, 0, -192108, 32347568] [2, 2] 18432  
2880.a2 2880n7 [0, 0, 0, -261228, 6994352] [2] 36864  
2880.a1 2880n8 [0, 0, 0, -3072108, 2072539568] [2] 36864  

Rank

sage: E.rank()
 

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

Modular form 2880.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.