Properties

Label 1155a
Number of curves $4$
Conductor $1155$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1155.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1155a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.d3 1155a1 [1, 1, 1, -11, -16] [2] 96 \(\Gamma_0(N)\)-optimal
1155.d2 1155a2 [1, 1, 1, -56, 128] [2, 2] 192  
1155.d1 1155a3 [1, 1, 1, -881, 9698] [2] 384  
1155.d4 1155a4 [1, 1, 1, 49, 674] [2] 384  

Rank

sage: E.rank()
 

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

Modular form 1155.2.a.d

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 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.