Properties

Label 1122k
Number of curves $4$
Conductor $1122$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1122.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1122k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.m4 1122k1 [1, 0, 0, -5847, -135063] [4] 2688 \(\Gamma_0(N)\)-optimal
1122.m2 1122k2 [1, 0, 0, -87767, -10014615] [2, 2] 5376  
1122.m1 1122k3 [1, 0, 0, -1404247, -640608535] [2] 10752  
1122.m3 1122k4 [1, 0, 0, -82007, -11384343] [2] 10752  

Rank

sage: E.rank()
 

The elliptic curves in class 1122k have rank \(0\).

Modular form 1122.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + 4q^{7} + q^{8} + q^{9} + 2q^{10} - q^{11} + q^{12} - 2q^{13} + 4q^{14} + 2q^{15} + q^{16} + q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.