Properties

Label 62400gy
Number of curves $6$
Conductor $62400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("62400.fz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400gy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.fz6 62400gy1 [0, 1, 0, 23967, -563937] [2] 294912 \(\Gamma_0(N)\)-optimal
62400.fz5 62400gy2 [0, 1, 0, -104033, -4787937] [2, 2] 589824  
62400.fz3 62400gy3 [0, 1, 0, -904033, 327212063] [2, 2] 1179648  
62400.fz2 62400gy4 [0, 1, 0, -1352033, -605075937] [2] 1179648  
62400.fz4 62400gy5 [0, 1, 0, -184033, 834812063] [2] 2359296  
62400.fz1 62400gy6 [0, 1, 0, -14424033, 21080412063] [4] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 62400gy have rank \(0\).

Modular form 62400.2.a.fz

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + 4q^{11} + q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.