Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("33640.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33640.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33640.f1 33640g4 [0, 0, 0, -695507, -184039394] [2] 430080  
33640.f2 33640g2 [0, 0, 0, -207727, 33803154] [2, 2] 215040  
33640.f3 33640g1 [0, 0, 0, -203522, 35339661] [4] 107520 \(\Gamma_0(N)\)-optimal
33640.f4 33640g3 [0, 0, 0, 212773, 153309254] [2] 430080  

Rank

sage: E.rank()
 

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

Modular form 33640.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{5} - 3q^{9} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.