Properties

Label 33600.db
Number of curves 4
Conductor 33600
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("33600.db1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.db1 33600ez4 [0, -1, 0, -180033, 29459937] [2] 196608  
33600.db2 33600ez2 [0, -1, 0, -12033, 395937] [2, 2] 98304  
33600.db3 33600ez1 [0, -1, 0, -4033, -92063] [2] 49152 \(\Gamma_0(N)\)-optimal
33600.db4 33600ez3 [0, -1, 0, 27967, 2435937] [2] 196608  

Rank

sage: E.rank()
 

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

Modular form 33600.2.a.db

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.