Properties

Label 11760cp
Number of curves 8
Conductor 11760
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("11760.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.ci8 11760cp1 [0, 1, 0, 1160, 47060] [2] 13824 \(\Gamma_0(N)\)-optimal
11760.ci6 11760cp2 [0, 1, 0, -14520, 605268] [2, 2] 27648  
11760.ci7 11760cp3 [0, 1, 0, -10600, -1378252] [2] 41472  
11760.ci5 11760cp4 [0, 1, 0, -53720, -4145772] [2] 55296  
11760.ci4 11760cp5 [0, 1, 0, -226200, 41332500] [2] 55296  
11760.ci3 11760cp6 [0, 1, 0, -261480, -51453900] [2, 2] 82944  
11760.ci1 11760cp7 [0, 1, 0, -4181480, -3292509900] [2] 165888  
11760.ci2 11760cp8 [0, 1, 0, -355560, -11225292] [2] 165888  

Rank

sage: E.rank()
 

The elliptic curves in class 11760cp have rank \(1\).

Modular form 11760.2.a.ci

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{9} - 2q^{13} + q^{15} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.