Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1122.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1122b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.c3 1122b1 [1, 1, 0, -8279, -264363] [2] 3840 \(\Gamma_0(N)\)-optimal
1122.c2 1122b2 [1, 1, 0, -31399, 1848805] [2, 2] 7680  
1122.c1 1122b3 [1, 1, 0, -483939, 129374577] [2] 15360  
1122.c4 1122b4 [1, 1, 0, 51221, 10028185] [2] 15360  

Rank

sage: E.rank()
 

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

Modular form 1122.2.a.c

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

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.