Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 11109i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11109.d6 11109i1 \([1, 0, 0, 518, 1043]\) \(103823/63\) \(-9326261007\) \([2]\) \(6336\) \(0.60223\) \(\Gamma_0(N)\)-optimal
11109.d5 11109i2 \([1, 0, 0, -2127, 7920]\) \(7189057/3969\) \(587554443441\) \([2, 2]\) \(12672\) \(0.94880\)  
11109.d3 11109i3 \([1, 0, 0, -20642, -1136307]\) \(6570725617/45927\) \(6798844274103\) \([2]\) \(25344\) \(1.2954\)  
11109.d2 11109i4 \([1, 0, 0, -25932, 1602855]\) \(13027640977/21609\) \(3198907525401\) \([2, 2]\) \(25344\) \(1.2954\)  
11109.d1 11109i5 \([1, 0, 0, -414747, 102772518]\) \(53297461115137/147\) \(21761275683\) \([2]\) \(50688\) \(1.6420\)  
11109.d4 11109i6 \([1, 0, 0, -17997, 2604252]\) \(-4354703137/17294403\) \(-2560192322829267\) \([2]\) \(50688\) \(1.6420\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 11109i do not have complex multiplication.

Modular form 11109.2.a.i

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

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.