Properties

Label 33600.dg
Number of curves 8
Conductor 33600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33600.dg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dg1 33600ey8 [0, -1, 0, -561972033, 5127858515937] [2] 5308416  
33600.dg2 33600ey6 [0, -1, 0, -35124033, 80127827937] [2, 2] 2654208  
33600.dg3 33600ey7 [0, -1, 0, -32564033, 92300627937] [2] 5308416  
33600.dg4 33600ey5 [0, -1, 0, -6972033, 6963515937] [2] 1769472  
33600.dg5 33600ey3 [0, -1, 0, -2356033, 1058643937] [2] 1327104  
33600.dg6 33600ey2 [0, -1, 0, -924033, -179172063] [2, 2] 884736  
33600.dg7 33600ey1 [0, -1, 0, -796033, -272996063] [2] 442368 \(\Gamma_0(N)\)-optimal
33600.dg8 33600ey4 [0, -1, 0, 3075967, -1319172063] [2] 1769472  

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.dg

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{7} + q^{9} + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.