Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.w1 47190y4 \([1, 0, 1, -144719, 20099792]\) \(189208196468929/10860320250\) \(19239719802410250\) \([2]\) \(414720\) \(1.8788\)  
47190.w2 47190y2 \([1, 0, 1, -24929, -1510324]\) \(967068262369/4928040\) \(8730323470440\) \([2]\) \(138240\) \(1.3295\)  
47190.w3 47190y1 \([1, 0, 1, -729, -48644]\) \(-24137569/561600\) \(-994908657600\) \([2]\) \(69120\) \(0.98289\) \(\Gamma_0(N)\)-optimal
47190.w4 47190y3 \([1, 0, 1, 6531, 1284292]\) \(17394111071/411937500\) \(-729772409437500\) \([2]\) \(207360\) \(1.5322\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.w

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.