Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.y4 47190u1 \([1, 0, 1, 132371, 40035752]\) \(144794100308831/474439680000\) \(-840498833940480000\) \([2]\) \(737280\) \(2.1225\) \(\Gamma_0(N)\)-optimal
47190.y3 47190u2 \([1, 0, 1, -1261549, 471035816]\) \(125337052492018849/18404100000000\) \(32603985800100000000\) \([2, 2]\) \(1474560\) \(2.4691\)  
47190.y2 47190u3 \([1, 0, 1, -5414269, -4384324408]\) \(9908022260084596129/1047363281250000\) \(1855467941894531250000\) \([2]\) \(2949120\) \(2.8157\)  
47190.y1 47190u4 \([1, 0, 1, -19411549, 32915975816]\) \(456612868287073618849/12544848030000\) \(22223963520874830000\) \([2]\) \(2949120\) \(2.8157\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.u

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