Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("33600.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.j1 33600l6 [0, -1, 0, -26880033, -53631540063] [2] 1179648  
33600.j2 33600l4 [0, -1, 0, -1680033, -837540063] [2, 2] 589824  
33600.j3 33600l5 [0, -1, 0, -1568033, -954132063] [2] 1179648  
33600.j4 33600l3 [0, -1, 0, -592033, 165915937] [2] 589824  
33600.j5 33600l2 [0, -1, 0, -112033, -11204063] [2, 2] 294912  
33600.j6 33600l1 [0, -1, 0, 15967, -1092063] [2] 147456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.j

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.