Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1155.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1155l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.m4 1155l1 [1, 0, 1, -3158, 4403] [2] 1920 \(\Gamma_0(N)\)-optimal
1155.m2 1155l2 [1, 0, 1, -35963, 2615681] [2, 2] 3840  
1155.m1 1155l3 [1, 0, 1, -575018, 167782133] [4] 7680  
1155.m3 1155l4 [1, 0, 1, -21788, 4702241] [2] 7680  

Rank

sage: E.rank()
 

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

Modular form 1155.2.a.m

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

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.