Properties

Label 33150.ba
Number of curves 2
Conductor 33150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33150.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33150.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33150.ba1 33150v1 [1, 0, 1, -340501, 75575648] [2] 368640 \(\Gamma_0(N)\)-optimal
33150.ba2 33150v2 [1, 0, 1, -52501, 199415648] [2] 737280  

Rank

sage: E.rank()
 

The elliptic curves in class 33150.ba have rank \(0\).

Modular form 33150.2.a.ba

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.