Properties

Label 10830.q
Number of curves 8
Conductor 10830
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("10830.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.q1 10830v8 [1, 1, 1, -1925401, 1027521599] [2] 165888  
10830.q2 10830v7 [1, 1, 1, -163721, 3402143] [2] 165888  
10830.q3 10830v6 [1, 1, 1, -120401, 15999599] [2, 2] 82944  
10830.q4 10830v4 [1, 1, 1, -104156, -12981481] [2] 55296  
10830.q5 10830v5 [1, 1, 1, -24736, 1279463] [2] 55296  
10830.q6 10830v2 [1, 1, 1, -6686, -193417] [2, 2] 27648  
10830.q7 10830v3 [1, 1, 1, -4881, 427503] [2] 41472  
10830.q8 10830v1 [1, 1, 1, 534, -14361] [2] 13824 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10830.q have rank \(1\).

Modular form 10830.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} - q^{12} - 2q^{13} - 4q^{14} + q^{15} + q^{16} + 6q^{17} + q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.