Properties

Label 33600.ej
Number of curves 4
Conductor 33600
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("33600.ej1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.ej1 33600ce4 [0, 1, 0, -180033, -29459937] [2] 196608  
33600.ej2 33600ce2 [0, 1, 0, -12033, -395937] [2, 2] 98304  
33600.ej3 33600ce1 [0, 1, 0, -4033, 92063] [2] 49152 \(\Gamma_0(N)\)-optimal
33600.ej4 33600ce3 [0, 1, 0, 27967, -2435937] [2] 196608  

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.ej

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} + q^{9} - 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.