Properties

Label 2880.x
Number of curves $6$
Conductor $2880$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.x1 2880s5 [0, 0, 0, -115212, 15052016] [4] 8192  
2880.x2 2880s3 [0, 0, 0, -7212, 234416] [2, 2] 4096  
2880.x3 2880s6 [0, 0, 0, -2892, 512624] [2] 8192  
2880.x4 2880s2 [0, 0, 0, -732, -1456] [2, 2] 2048  
2880.x5 2880s1 [0, 0, 0, -552, -4984] [2] 1024 \(\Gamma_0(N)\)-optimal
2880.x6 2880s4 [0, 0, 0, 2868, -11536] [2] 4096  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 2880.x do not have complex multiplication.

Modular form 2880.2.a.x

sage: E.q_eigenform(10)
 
\( q + q^{5} - 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.