Properties

Label 33327.k
Number of curves 6
Conductor 33327
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("33327.k1")
sage: E.isogeny_class()

Elliptic curves in class 33327.k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
33327.k1 33327m6 [1, -1, 0, -3732723, -2774857986] 2 405504  
33327.k2 33327m4 [1, -1, 0, -233388, -43277085] 4 202752  
33327.k3 33327m3 [1, -1, 0, -185778, 30680289] 2 202752  
33327.k4 33327m5 [1, -1, 0, -161973, -70314804] 2 405504  
33327.k5 33327m2 [1, -1, 0, -19143, -213840] 4 101376  
33327.k6 33327m1 [1, -1, 0, 4662, -28161] 2 50688 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 33327.k have rank \(0\).

Modular form 33327.2.a.k

sage: E.q_eigenform(10)
\( q + q^{2} - q^{4} - 2q^{5} + q^{7} - 3q^{8} - 2q^{10} + 4q^{11} - 2q^{13} + q^{14} - q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.