Properties

Label 1155.j
Number of curves $4$
Conductor $1155$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1155.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1155.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.j1 1155c3 [1, 1, 0, -2123, -38142] [2] 1152  
1155.j2 1155c2 [1, 1, 0, -248, 483] [2, 2] 576  
1155.j3 1155c1 [1, 1, 0, -203, 1032] [2] 288 \(\Gamma_0(N)\)-optimal
1155.j4 1155c4 [1, 1, 0, 907, 4872] [2] 1152  

Rank

sage: E.rank()
 

The elliptic curves in class 1155.j have rank \(0\).

Modular form 1155.2.a.j

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

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 LMFDB 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 LMFDB labels.