Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.r1 47190r4 \([1, 1, 0, -784687, 267194371]\) \(30161840495801041/2799263610\) \(4959066240195210\) \([2]\) \(983040\) \(2.0498\)  
47190.r2 47190r3 \([1, 1, 0, -288587, -56846049]\) \(1500376464746641/83599963590\) \(148102435097463990\) \([2]\) \(983040\) \(2.0498\)  
47190.r3 47190r2 \([1, 1, 0, -52637, 3509961]\) \(9104453457841/2226896100\) \(3945082281812100\) \([2, 2]\) \(491520\) \(1.7033\)  
47190.r4 47190r1 \([1, 1, 0, 7863, 351861]\) \(30342134159/47190000\) \(-83599963590000\) \([2]\) \(245760\) \(1.3567\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.r

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