Properties

Label 1155n
Number of curves 2
Conductor 1155
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1155.c1")
sage: E.isogeny_class()

Elliptic curves in class 1155n

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1155.c2 1155n1 [0, 1, 1, -8940, 378056] 5 6000 \(\Gamma_0(N)\)-optimal
1155.c1 1155n2 [0, 1, 1, -26790, -31917424] 1 30000  

Rank

sage: E.rank()

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

Modular form 1155.2.a.c

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

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.