Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.i4 47190s1 \([1, 1, 0, -10247284907, -409557128503299]\) \(-67172890180943415009710808721/2029083623424000000000000\) \(-3594645412996644864000000000000\) \([2]\) \(139345920\) \(4.6409\) \(\Gamma_0(N)\)-optimal
47190.i3 47190s2 \([1, 1, 0, -165127284907, -25827192712503299]\) \(281076231077501634961715630808721/245403072288481536000000\) \(434746512146454638397696000000\) \([2, 2]\) \(278691840\) \(4.9875\)  
47190.i2 47190s3 \([1, 1, 0, -166298564907, -25442206797607299]\) \(287099942490903701230558394328721/8299347173197257908489616000\) \(14702799777496507417621772610576000\) \([2]\) \(557383680\) \(5.3340\)  
47190.i1 47190s4 \([1, 1, 0, -2642036004907, -1652937758403399299]\) \(1151287518770166280399859009187288721/877598977782384000\) \(1554720122679137981424000\) \([2]\) \(557383680\) \(5.3340\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.s

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