Properties

Label 33150.n
Number of curves 4
Conductor 33150
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33150.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33150.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33150.n1 33150q4 [1, 0, 1, -1915501, 1018505648] [2] 1105920  
33150.n2 33150q3 [1, 0, 1, -1605501, -779074352] [2] 1105920  
33150.n3 33150q2 [1, 0, 1, -160501, 4115648] [2, 2] 552960  
33150.n4 33150q1 [1, 0, 1, 39499, 515648] [2] 276480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33150.n have rank \(1\).

Modular form 33150.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - 4q^{7} - q^{8} + q^{9} - 4q^{11} + q^{12} - q^{13} + 4q^{14} + q^{16} + q^{17} - q^{18} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.