Properties

Label 5544.c
Number of curves $4$
Conductor $5544$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5544.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5544.c1 5544t3 \([0, 0, 0, -5762091, 3774890054]\) \(14171198121996897746/4077720290568771\) \(6088003772056850552832\) \([2]\) \(368640\) \(2.8864\)  
5544.c2 5544t2 \([0, 0, 0, -5282931, 4673123390]\) \(21843440425782779332/3100814593569\) \(2314745690840884224\) \([2, 2]\) \(184320\) \(2.5399\)  
5544.c3 5544t1 \([0, 0, 0, -5282751, 4673457794]\) \(87364831012240243408/1760913\) \(328628627712\) \([4]\) \(92160\) \(2.1933\) \(\Gamma_0(N)\)-optimal
5544.c4 5544t4 \([0, 0, 0, -4806651, 5549954870]\) \(-8226100326647904626/4152140742401883\) \(-6199112911280072103936\) \([2]\) \(368640\) \(2.8864\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5544.c have rank \(0\).

Complex multiplication

The elliptic curves in class 5544.c do not have complex multiplication.

Modular form 5544.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} - q^{11} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.