Properties

Label 58800.ji
Number of curves $6$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58800.ji1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.ji

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.ji1 58800dj6 [0, 1, 0, -12838408, -17709656812] [2] 2359296  
58800.ji2 58800dj4 [0, 1, 0, -833408, -254386812] [2, 2] 1179648  
58800.ji3 58800dj2 [0, 1, 0, -220908, 35938188] [2, 2] 589824  
58800.ji4 58800dj1 [0, 1, 0, -214783, 38241188] [2] 294912 \(\Gamma_0(N)\)-optimal
58800.ji5 58800dj3 [0, 1, 0, 293592, 178969188] [2] 1179648  
58800.ji6 58800dj5 [0, 1, 0, 1371592, -1370116812] [2] 2359296  

Rank

sage: E.rank()
 

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

Modular form 58800.2.a.ji

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + 4q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.