Properties

Label 33150.l
Number of curves 8
Conductor 33150
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("33150.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33150.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33150.l1 33150b8 [1, 1, 0, -164775000150, -25744606186158000] [2] 79626240  
33150.l2 33150b6 [1, 1, 0, -10298437650, -402262678345500] [2, 2] 39813120  
33150.l3 33150b7 [1, 1, 0, -10279763150, -403794192765000] [2] 79626240  
33150.l4 33150b5 [1, 1, 0, -2034331650, -35313074887500] [2] 26542080  
33150.l5 33150b3 [1, 1, 0, -644819650, -6261614367500] [2] 19906560  
33150.l6 33150b2 [1, 1, 0, -138931650, -443401087500] [2, 2] 13271040  
33150.l7 33150b1 [1, 1, 0, -52403650, 140576384500] [2] 6635520 \(\Gamma_0(N)\)-optimal
33150.l8 33150b4 [1, 1, 0, 372020350, -2946554935500] [2] 26542080  

Rank

sage: E.rank()
 

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

Modular form 33150.2.a.l

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.