Properties

Label 44352.dx
Number of curves $4$
Conductor $44352$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dx1")
 
E.isogeny_class()
 

Elliptic curves in class 44352.dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44352.dx1 44352bn4 \([0, 0, 0, -1369164, 616639088]\) \(2970658109581346/2139291\) \(204412438315008\) \([2]\) \(524288\) \(2.0578\)  
44352.dx2 44352bn3 \([0, 0, 0, -197004, -19989520]\) \(8849350367426/3314597517\) \(316714724870455296\) \([2]\) \(524288\) \(2.0578\)  
44352.dx3 44352bn2 \([0, 0, 0, -86124, 9504560]\) \(1478729816932/38900169\) \(1858484515700736\) \([2, 2]\) \(262144\) \(1.7112\)  
44352.dx4 44352bn1 \([0, 0, 0, 996, 478928]\) \(9148592/8301447\) \(-99151951675392\) \([2]\) \(131072\) \(1.3647\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44352.dx have rank \(1\).

Complex multiplication

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

Modular form 44352.2.a.dx

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.