Properties

Label 1155m
Number of curves $6$
Conductor $1155$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1155.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1155m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.f6 1155m1 [1, 0, 0, 35, -23128] [4] 960 \(\Gamma_0(N)\)-optimal
1155.f5 1155m2 [1, 0, 0, -11970, -496125] [2, 4] 1920  
1155.f2 1155m3 [1, 0, 0, -190575, -32037768] [2, 2] 3840  
1155.f4 1155m4 [1, 0, 0, -25445, 821730] [4] 3840  
1155.f1 1155m5 [1, 0, 0, -3049200, -2049655293] [2] 7680  
1155.f3 1155m6 [1, 0, 0, -189630, -32370975] [2] 7680  

Rank

sage: E.rank()
 

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

Modular form 1155.2.a.f

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.