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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 109554j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
109554.m2 109554j1 \([1, 0, 1, 62925, -261936434]\) \(31047965207/33416146944\) \(-29656953417636900864\) \([2]\) \(4423680\) \(2.4154\) \(\Gamma_0(N)\)-optimal
109554.m1 109554j2 \([1, 0, 1, -5779955, -5228384434]\) \(24061727981584873/621029198016\) \(551165699247677896896\) \([2]\) \(8847360\) \(2.7619\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 109554.2.a.j

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