Properties

Label 33800a
Number of curves 4
Conductor 33800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33800.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33800a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.o3 33800a1 [0, 0, 0, -97175, 11534250] [2] 129024 \(\Gamma_0(N)\)-optimal
33800.o2 33800a2 [0, 0, 0, -181675, -11534250] [2, 2] 258048  
33800.o4 33800a3 [0, 0, 0, 663325, -88429250] [2] 516096  
33800.o1 33800a4 [0, 0, 0, -2378675, -1411023250] [2] 516096  

Rank

sage: E.rank()
 

The elliptic curves in class 33800a have rank \(1\).

Modular form 33800.2.a.o

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.