Properties

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

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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 order Modular degree Optimality
1155.e1 1155e5 [1, 1, 1, -13250, -592540] 2 2048  
1155.e2 1155e3 [1, 1, 1, -875, -8440] 4 1024  
1155.e3 1155e2 [1, 1, 1, -270, 1482] 8 512  
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.