Properties

Label 190575be
Number of curves 4
Conductor 190575
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("190575.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 190575be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190575.bp3 190575be1 [1, -1, 1, -68630, 6573372] [2] 1105920 \(\Gamma_0(N)\)-optimal
190575.bp2 190575be2 [1, -1, 1, -204755, -27457878] [2, 2] 2211840  
190575.bp4 190575be3 [1, -1, 1, 475870, -171750378] [2] 4423680  
190575.bp1 190575be4 [1, -1, 1, -3063380, -2062798878] [2] 4423680  

Rank

sage: E.rank()
 

The elliptic curves in class 190575be have rank \(0\).

Modular form 190575.2.a.bp

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.