Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("33600.dz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.dz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dz1 33600gi4 [0, 1, 0, -2150433, -1214488737] [2] 393216  
33600.dz2 33600gi6 [0, 1, 0, -1462433, 673687263] [2] 786432  
33600.dz3 33600gi3 [0, 1, 0, -166433, -9304737] [2, 2] 393216  
33600.dz4 33600gi2 [0, 1, 0, -134433, -19000737] [2, 2] 196608  
33600.dz5 33600gi1 [0, 1, 0, -6433, -440737] [2] 98304 \(\Gamma_0(N)\)-optimal
33600.dz6 33600gi5 [0, 1, 0, 617567, -71240737] [2] 786432  

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.dz

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} + q^{9} - 4q^{11} + 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.