Properties

Label 62400.cm
Number of curves $6$
Conductor $62400$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("62400.cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.cm1 62400z6 [0, -1, 0, -14424033, -21080412063] [2] 2359296  
62400.cm2 62400z4 [0, -1, 0, -1352033, 605075937] [2] 1179648  
62400.cm3 62400z3 [0, -1, 0, -904033, -327212063] [2, 2] 1179648  
62400.cm4 62400z5 [0, -1, 0, -184033, -834812063] [4] 2359296  
62400.cm5 62400z2 [0, -1, 0, -104033, 4787937] [2, 2] 589824  
62400.cm6 62400z1 [0, -1, 0, 23967, 563937] [2] 294912 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.cm have rank \(2\).

Modular form 62400.2.a.cm

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.