Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("33600.dr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dr5 33600ba1 [0, -1, 0, -6433, 440737] [2] 98304 \(\Gamma_0(N)\)-optimal
33600.dr4 33600ba2 [0, -1, 0, -134433, 19000737] [2, 2] 196608  
33600.dr3 33600ba3 [0, -1, 0, -166433, 9304737] [2, 2] 393216  
33600.dr1 33600ba4 [0, -1, 0, -2150433, 1214488737] [2] 393216  
33600.dr6 33600ba5 [0, -1, 0, 617567, 71240737] [2] 786432  
33600.dr2 33600ba6 [0, -1, 0, -1462433, -673687263] [2] 786432  

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.dr

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{7} + q^{9} + 4q^{11} + 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.