Properties

Label 33640h
Number of curves 4
Conductor 33640
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33640.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33640h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33640.e3 33640h1 [0, 0, 0, -1682, 24389] [2] 25088 \(\Gamma_0(N)\)-optimal
33640.e2 33640h2 [0, 0, 0, -5887, -146334] [2, 2] 50176  
33640.e4 33640h3 [0, 0, 0, 10933, -829226] [2] 100352  
33640.e1 33640h4 [0, 0, 0, -89987, -10389714] [2] 100352  

Rank

sage: E.rank()
 

The elliptic curves in class 33640h have rank \(1\).

Modular form 33640.2.a.e

sage: E.q_eigenform(10)
 
\( q + q^{5} - 4q^{7} - 3q^{9} - 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.