Properties

Label 11109i
Number of curves 6
Conductor 11109
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("11109.d1")
sage: E.isogeny_class()

Elliptic curves in class 11109i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
11109.d6 11109i1 [1, 0, 0, 518, 1043] 2 6336 \(\Gamma_0(N)\)-optimal
11109.d5 11109i2 [1, 0, 0, -2127, 7920] 4 12672  
11109.d3 11109i3 [1, 0, 0, -20642, -1136307] 2 25344  
11109.d2 11109i4 [1, 0, 0, -25932, 1602855] 4 25344  
11109.d1 11109i5 [1, 0, 0, -414747, 102772518] 2 50688  
11109.d4 11109i6 [1, 0, 0, -17997, 2604252] 2 50688  

Rank

sage: E.rank()

The elliptic curves in class 11109i have rank \(0\).

Modular form 11109.2.a.d

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} + q^{7} + 3q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} - 2q^{13} - q^{14} + 2q^{15} - q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.