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Properties

Label 11109g
Number of curves $2$
Conductor $11109$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 11109g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11109.h2 11109g1 \([1, 0, 1, 280094, 249871151]\) \(1349232625/15752961\) \(-28373487631072841943\) \([2]\) \(194304\) \(2.4136\) \(\Gamma_0(N)\)-optimal
11109.h1 11109g2 \([1, 0, 1, -4647541, 3594749789]\) \(6163717745375/466948881\) \(841046219780319672903\) \([2]\) \(388608\) \(2.7602\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11109.2.a.g

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.