Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1122.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1122h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.h3 1122h1 [1, 1, 1, -387, 2769] [4] 384 \(\Gamma_0(N)\)-optimal
1122.h2 1122h2 [1, 1, 1, -407, 2441] [2, 2] 768  
1122.h1 1122h3 [1, 1, 1, -1937, -31219] [2] 1536  
1122.h4 1122h4 [1, 1, 1, 803, 15509] [2] 1536  

Rank

sage: E.rank()
 

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

Modular form 1122.2.a.h

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.