Properties

Label 53900o
Number of curves 4
Conductor 53900
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("53900.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53900o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53900.b4 53900o1 [0, 1, 0, -55533, -4952312] [2] 248832 \(\Gamma_0(N)\)-optimal
53900.b3 53900o2 [0, 1, 0, -122908, 9331188] [2] 497664  
53900.b2 53900o3 [0, 1, 0, -545533, 152950188] [2] 746496  
53900.b1 53900o4 [0, 1, 0, -8697908, 9870581188] [2] 1492992  

Rank

sage: E.rank()
 

The elliptic curves in class 53900o have rank \(1\).

Modular form 53900.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{9} - q^{11} - 4q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.