Properties

Label 15210.bq
Number of curves $6$
Conductor $15210$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15210.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15210.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15210.bq1 15210bn5 [1, -1, 1, -13711847, 19546461861] [2] 688128  
15210.bq2 15210bn3 [1, -1, 1, -1285277, -560081271] [2] 344064  
15210.bq3 15210bn4 [1, -1, 1, -859397, 303773721] [2, 2] 344064  
15210.bq4 15210bn6 [1, -1, 1, -174947, 773853981] [2] 688128  
15210.bq5 15210bn2 [1, -1, 1, -98897, -4380879] [2, 2] 172032  
15210.bq6 15210bn1 [1, -1, 1, 22783, -535791] [4] 86016 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15210.bq have rank \(0\).

Modular form 15210.2.a.bq

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.