Properties

Label 33600.eo
Number of curves $8$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33600.eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.eo1 33600cc8 [0, 1, 0, -10321633, 8026548863] [2] 2654208  
33600.eo2 33600cc5 [0, 1, 0, -9217633, 10768452863] [2] 884736  
33600.eo3 33600cc6 [0, 1, 0, -4321633, -3367451137] [2, 2] 1327104  
33600.eo4 33600cc3 [0, 1, 0, -4289633, -3421051137] [2] 663552  
33600.eo5 33600cc2 [0, 1, 0, -577633, 167172863] [2, 2] 442368  
33600.eo6 33600cc4 [0, 1, 0, -129633, 420292863] [2] 884736  
33600.eo7 33600cc1 [0, 1, 0, -65633, -2299137] [2] 221184 \(\Gamma_0(N)\)-optimal
33600.eo8 33600cc7 [0, 1, 0, 1166367, -11330539137] [2] 2654208  

Rank

sage: E.rank()
 

The elliptic curves in class 33600.eo have rank \(0\).

Modular form 33600.2.a.eo

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.