Properties

Label 8880.ba
Number of curves $6$
Conductor $8880$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8880.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8880.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8880.ba1 8880ba3 [0, 1, 0, -5456080, -4907160172] [2] 165888  
8880.ba2 8880ba5 [0, 1, 0, -4850000, 4091635860] [4] 331776  
8880.ba3 8880ba4 [0, 1, 0, -469200, -14049900] [2, 4] 165888  
8880.ba4 8880ba2 [0, 1, 0, -341200, -76667500] [2, 2] 82944  
8880.ba5 8880ba1 [0, 1, 0, -13520, -2087532] [2] 41472 \(\Gamma_0(N)\)-optimal
8880.ba6 8880ba6 [0, 1, 0, 1863600, -110161260] [4] 331776  

Rank

sage: E.rank()
 

The elliptic curves in class 8880.ba have rank \(1\).

Modular form 8880.2.a.ba

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{9} - 4q^{11} - 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.