Properties

Label 33600x
Number of curves $6$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33600.dp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dp4 33600x1 [0, -1, 0, -17533, 899437] [2] 49152 \(\Gamma_0(N)\)-optimal
33600.dp3 33600x2 [0, -1, 0, -18033, 845937] [2, 2] 98304  
33600.dp5 33600x3 [0, -1, 0, 23967, 4163937] [2] 196608  
33600.dp2 33600x4 [0, -1, 0, -68033, -5904063] [2, 2] 196608  
33600.dp6 33600x5 [0, -1, 0, 111967, -32004063] [4] 393216  
33600.dp1 33600x6 [0, -1, 0, -1048033, -412604063] [2] 393216  

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.dp

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.