Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("33600.he1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.he

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.he1 33600gt6 [0, 1, 0, -26880033, 53631540063] [2] 1179648  
33600.he2 33600gt4 [0, 1, 0, -1680033, 837540063] [2, 2] 589824  
33600.he3 33600gt5 [0, 1, 0, -1568033, 954132063] [2] 1179648  
33600.he4 33600gt3 [0, 1, 0, -592033, -165915937] [2] 589824  
33600.he5 33600gt2 [0, 1, 0, -112033, 11204063] [2, 2] 294912  
33600.he6 33600gt1 [0, 1, 0, 15967, 1092063] [2] 147456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.he

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.