Properties

Label 33620a
Number of curves 4
Conductor 33620
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("33620.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33620a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33620.a3 33620a1 [0, -1, 0, -2241, 28826] [2] 34560 \(\Gamma_0(N)\)-optimal
33620.a4 33620a2 [0, -1, 0, 6164, 186840] [2] 69120  
33620.a1 33620a3 [0, -1, 0, -69481, -7024650] [2] 103680  
33620.a2 33620a4 [0, -1, 0, -61076, -8796424] [2] 207360  

Rank

sage: E.rank()
 

The elliptic curves in class 33620a have rank \(0\).

Modular form 33620.2.a.a

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} - 2q^{7} + q^{9} - 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.