Properties

Label 1170d
Number of curves $6$
Conductor $1170$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1170.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1170d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1170.a6 1170d1 [1, -1, 0, 135, -275] [2] 512 \(\Gamma_0(N)\)-optimal
1170.a5 1170d2 [1, -1, 0, -585, -1859] [2, 2] 1024  
1170.a2 1170d3 [1, -1, 0, -7605, -253175] [2] 2048  
1170.a3 1170d4 [1, -1, 0, -5085, 139441] [2, 2] 2048  
1170.a1 1170d5 [1, -1, 0, -81135, 8915611] [2] 4096  
1170.a4 1170d6 [1, -1, 0, -1035, 352471] [2] 4096  

Rank

sage: E.rank()
 

The elliptic curves in class 1170d have rank \(1\).

Modular form 1170.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} + q^{13} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.