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Properties

Label 109554l
Number of curves $2$
Conductor $109554$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 109554l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
109554.k2 109554l1 \([1, 0, 1, -8783080, 10039637606]\) \(-84429456495634873/210012812784\) \(-186387144402963857904\) \([2]\) \(8847360\) \(2.7672\) \(\Gamma_0(N)\)-optimal
109554.k1 109554l2 \([1, 0, 1, -140613060, 641768901766]\) \(346441988636642533753/2135645676\) \(1895393398761733356\) \([2]\) \(17694720\) \(3.1138\)  

Rank

sage: E.rank()
 

The elliptic curves in class 109554l have rank \(1\).

Complex multiplication

The elliptic curves in class 109554l do not have complex multiplication.

Modular form 109554.2.a.l

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