Properties

Label 109554.r
Number of curves $4$
Conductor $109554$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 109554.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
109554.r1 109554q3 \([1, 1, 1, -411328, 101366237]\) \(8671983378625/82308\) \(73048652975748\) \([2]\) \(1101600\) \(1.8225\)  
109554.r2 109554q4 \([1, 1, 1, -401718, 106340373]\) \(-8078253774625/846825858\) \(-751561066140983298\) \([2]\) \(2203200\) \(2.1691\)  
109554.r3 109554q1 \([1, 1, 1, -7708, -23107]\) \(57066625/32832\) \(29138520854592\) \([2]\) \(367200\) \(1.2732\) \(\Gamma_0(N)\)-optimal
109554.r4 109554q2 \([1, 1, 1, 30732, -146115]\) \(3616805375/2105352\) \(-1868507649800712\) \([2]\) \(734400\) \(1.6198\)  

Rank

sage: E.rank()
 

The elliptic curves in class 109554.r have rank \(0\).

Complex multiplication

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

Modular form 109554.2.a.r

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.