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Properties

Label 47190.bn
Number of curves $4$
Conductor $47190$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 47190.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.bn1 47190bq4 \([1, 1, 1, -4615971, 3815255379]\) \(6139836723518159689/3799803150\) \(6731583068217150\) \([2]\) \(1474560\) \(2.3580\)  
47190.bn2 47190bq3 \([1, 1, 1, -649591, -116167237]\) \(17111482619973769/6627044531250\) \(11740213636825781250\) \([2]\) \(1474560\) \(2.3580\)  
47190.bn3 47190bq2 \([1, 1, 1, -290221, 58774079]\) \(1525998818291689/37268302500\) \(66023071245202500\) \([2, 2]\) \(737280\) \(2.0115\)  
47190.bn4 47190bq1 \([1, 1, 1, 2599, 2904023]\) \(1095912791/2055596400\) \(-3641614413980400\) \([2]\) \(368640\) \(1.6649\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47190.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 47190.bn do not have complex multiplication.

Modular form 47190.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - 4 q^{14} + q^{15} + q^{16} - 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.