Properties

Label 33600.ce
Number of curves 6
Conductor 33600
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("33600.ce1")
sage: E.isogeny_class()

Elliptic curves in class 33600.ce

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
33600.ce1 33600em6 [0, -1, 0, -1254433, 541196737] 2 262144  
33600.ce2 33600em4 [0, -1, 0, -78433, 8468737] 4 131072  
33600.ce3 33600em3 [0, -1, 0, -62433, -5947263] 2 131072  
33600.ce4 33600em5 [0, -1, 0, -54433, 13724737] 2 262144  
33600.ce5 33600em2 [0, -1, 0, -6433, 44737] 4 65536  
33600.ce6 33600em1 [0, -1, 0, 1567, 4737] 2 32768 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

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

Modular form 33600.2.a.ce

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.