Properties

Label 53550dx
Number of curves $4$
Conductor $53550$
CM no
Rank $1$
Graph

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

Elliptic curves in class 53550dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53550.ec4 53550dx1 \([1, -1, 1, 220, -340153]\) \(103823/4386816\) \(-49968576000000\) \([2]\) \(196608\) \(1.3074\) \(\Gamma_0(N)\)-optimal
53550.ec3 53550dx2 \([1, -1, 1, -71780, -7252153]\) \(3590714269297/73410624\) \(836192889000000\) \([2, 2]\) \(393216\) \(1.6540\)  
53550.ec2 53550dx3 \([1, -1, 1, -152780, 12187847]\) \(34623662831857/14438442312\) \(164462881960125000\) \([2]\) \(786432\) \(2.0006\)  
53550.ec1 53550dx4 \([1, -1, 1, -1142780, -469924153]\) \(14489843500598257/6246072\) \(71146663875000\) \([2]\) \(786432\) \(2.0006\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53550dx have rank \(1\).

Complex multiplication

The elliptic curves in class 53550dx do not have complex multiplication.

Modular form 53550.2.a.dx

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} + 6q^{13} + q^{14} + q^{16} + q^{17} + O(q^{20})\)  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 Cremona 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 Cremona labels.