Properties

Label 880j
Number of curves 4
Conductor 880
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("880.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 880j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
880.j4 880j1 [0, -1, 0, -45, -100] [2] 144 \(\Gamma_0(N)\)-optimal
880.j3 880j2 [0, -1, 0, -100, 252] [2] 288  
880.j2 880j3 [0, -1, 0, -445, 3720] [2] 432  
880.j1 880j4 [0, -1, 0, -7100, 232652] [2] 864  

Rank

sage: E.rank()
 

The elliptic curves in class 880j have rank \(0\).

Modular form 880.2.a.j

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{5} + 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20}) \)

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.