Properties

Label 190575ed
Number of curves $6$
Conductor $190575$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("190575.dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 190575ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190575.dh4 190575ed1 [1, -1, 0, -7215192, 7461440091] [2] 5898240 \(\Gamma_0(N)\)-optimal
190575.dh3 190575ed2 [1, -1, 0, -7351317, 7165368216] [2, 2] 11796480  
190575.dh5 190575ed3 [1, -1, 0, 6941808, 31649491341] [2] 23592960  
190575.dh2 190575ed4 [1, -1, 0, -23822442, -36268988409] [2, 2] 23592960  
190575.dh6 190575ed5 [1, -1, 0, 49548933, -215662000284] [2] 47185920  
190575.dh1 190575ed6 [1, -1, 0, -360731817, -2636872454034] [2] 47185920  

Rank

sage: E.rank()
 

The elliptic curves in class 190575ed have rank \(1\).

Modular form 190575.2.a.dh

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.