Properties

Label 44352.ep
Number of curves $4$
Conductor $44352$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ep1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44352.ep

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44352.ep1 44352co4 \([0, 0, 0, -23048364, 30199120432]\) \(14171198121996897746/4077720290568771\) \(389632241411638435381248\) \([2]\) \(5898240\) \(3.2330\)  
44352.ep2 44352co2 \([0, 0, 0, -21131724, 37384987120]\) \(21843440425782779332/3100814593569\) \(148143724213816590336\) \([2, 2]\) \(2949120\) \(2.8864\)  
44352.ep3 44352co1 \([0, 0, 0, -21131004, 37387662352]\) \(87364831012240243408/1760913\) \(21032232173568\) \([2]\) \(1474560\) \(2.5399\) \(\Gamma_0(N)\)-optimal
44352.ep4 44352co3 \([0, 0, 0, -19226604, 44399638960]\) \(-8226100326647904626/4152140742401883\) \(-396743226321924614651904\) \([2]\) \(5898240\) \(3.2330\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44352.ep have rank \(0\).

Complex multiplication

The elliptic curves in class 44352.ep do not have complex multiplication.

Modular form 44352.2.a.ep

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.