Properties

Label 33800.e
Number of curves 2
Conductor 33800
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33800.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33800.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.e1 33800u1 [0, 1, 0, -85908, -9569312] [2] 129024 \(\Gamma_0(N)\)-optimal
33800.e2 33800u2 [0, 1, 0, -1408, -27483312] [2] 258048  

Rank

sage: E.rank()
 

The elliptic curves in class 33800.e have rank \(2\).

Modular form 33800.2.a.e

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.