Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 5544.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5544.u1 5544j3 \([0, 0, 0, -2259, -40770]\) \(1707831108/26411\) \(19715705856\) \([2]\) \(4096\) \(0.77669\)  
5544.u2 5544j2 \([0, 0, 0, -279, 810]\) \(12869712/5929\) \(1106493696\) \([2, 2]\) \(2048\) \(0.43011\)  
5544.u3 5544j1 \([0, 0, 0, -234, 1377]\) \(121485312/77\) \(898128\) \([2]\) \(1024\) \(0.083538\) \(\Gamma_0(N)\)-optimal
5544.u4 5544j4 \([0, 0, 0, 981, 6102]\) \(139863132/102487\) \(-76506135552\) \([2]\) \(4096\) \(0.77669\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5544.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{7} + q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.