Properties

Label 2880i
Number of curves 4
Conductor 2880
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2880.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.m3 2880i1 [0, 0, 0, -48, -88] [2] 384 \(\Gamma_0(N)\)-optimal
2880.m4 2880i2 [0, 0, 0, 132, -592] [2] 768  
2880.m1 2880i3 [0, 0, 0, -1488, 22088] [2] 1152  
2880.m2 2880i4 [0, 0, 0, -1308, 27632] [2] 2304  

Rank

sage: E.rank()
 

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

Modular form 2880.2.a.m

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.