Properties

Label 33600gg
Number of curves $6$
Conductor $33600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33600.dx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600gg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dx4 33600gg1 [0, 1, 0, -17533, -899437] [2] 49152 \(\Gamma_0(N)\)-optimal
33600.dx3 33600gg2 [0, 1, 0, -18033, -845937] [2, 2] 98304  
33600.dx5 33600gg3 [0, 1, 0, 23967, -4163937] [2] 196608  
33600.dx2 33600gg4 [0, 1, 0, -68033, 5904063] [2, 2] 196608  
33600.dx6 33600gg5 [0, 1, 0, 111967, 32004063] [2] 393216  
33600.dx1 33600gg6 [0, 1, 0, -1048033, 412604063] [4] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 33600gg have rank \(1\).

Modular form 33600.2.a.dx

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} + q^{9} - 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.