Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1122.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1122m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.j3 1122m1 [1, 0, 0, -205448, -35497920] [6] 11520 \(\Gamma_0(N)\)-optimal
1122.j4 1122m2 [1, 0, 0, -41608, -90515392] [6] 23040  
1122.j1 1122m3 [1, 0, 0, -16594568, -26020768704] [2] 34560  
1122.j2 1122m4 [1, 0, 0, -16594408, -26021295520] [2] 69120  

Rank

sage: E.rank()
 

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

Modular form 1122.2.a.j

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.