Properties

Label 58800fj
Number of curves 4
Conductor 58800
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("58800.bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.bx3 58800fj1 [0, -1, 0, -49408, 4021312] [2] 294912 \(\Gamma_0(N)\)-optimal
58800.bx2 58800fj2 [0, -1, 0, -147408, -16754688] [2, 2] 589824  
58800.bx4 58800fj3 [0, -1, 0, 342592, -104954688] [2] 1179648  
58800.bx1 58800fj4 [0, -1, 0, -2205408, -1259786688] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 58800fj have rank \(1\).

Modular form 58800.2.a.bx

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.