Properties

Label 33813.i
Number of curves $6$
Conductor $33813$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33813.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33813.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33813.i1 33813n6 [1, -1, 0, -52472628, 146291618079] [2] 2359296  
33813.i2 33813n4 [1, -1, 0, -3612843, 1793689920] [2, 2] 1179648  
33813.i3 33813n2 [1, -1, 0, -1414998, -626137425] [2, 2] 589824  
33813.i4 33813n1 [1, -1, 0, -1401993, -638598816] [2] 294912 \(\Gamma_0(N)\)-optimal
33813.i5 33813n3 [1, -1, 0, 574767, -2248591806] [2] 1179648  
33813.i6 33813n5 [1, -1, 0, 10081422, 12138337701] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 33813.i have rank \(1\).

Modular form 33813.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} + 4q^{11} + q^{13} - q^{16} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.