Properties

Label 33600.fm
Number of curves 6
Conductor 33600
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("33600.fm1")
sage: E.isogeny_class()

Elliptic curves in class 33600.fm

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
33600.fm1 33600dd6 [0, 1, 0, -1254433, -541196737] 2 262144  
33600.fm2 33600dd4 [0, 1, 0, -78433, -8468737] 4 131072  
33600.fm3 33600dd3 [0, 1, 0, -62433, 5947263] 2 131072  
33600.fm4 33600dd5 [0, 1, 0, -54433, -13724737] 2 262144  
33600.fm5 33600dd2 [0, 1, 0, -6433, -44737] 4 65536  
33600.fm6 33600dd1 [0, 1, 0, 1567, -4737] 2 32768 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

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

Modular form 33600.2.a.fm

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.