Properties

Label 1155.e
Number of curves $6$
Conductor $1155$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1155.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1155.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.e1 1155e5 [1, 1, 1, -13250, -592540] [2] 2048  
1155.e2 1155e3 [1, 1, 1, -875, -8440] [2, 2] 1024  
1155.e3 1155e2 [1, 1, 1, -270, 1482] [2, 4] 512  
1155.e4 1155e1 [1, 1, 1, -265, 1550] [4] 256 \(\Gamma_0(N)\)-optimal
1155.e5 1155e4 [1, 1, 1, 255, 7152] [4] 1024  
1155.e6 1155e6 [1, 1, 1, 1820, -47248] [2] 2048  

Rank

sage: E.rank()
 

The elliptic curves in class 1155.e have rank \(1\).

Modular form 1155.2.a.e

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.