Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.h3 47190h1 \([1, 1, 0, -7988, 195408]\) \(31824875809/8785920\) \(15564793221120\) \([2]\) \(138240\) \(1.2388\) \(\Gamma_0(N)\)-optimal
47190.h2 47190h2 \([1, 1, 0, -46708, -3746288]\) \(6361447449889/294465600\) \(521663772801600\) \([2, 2]\) \(276480\) \(1.5854\)  
47190.h4 47190h3 \([1, 1, 0, 25892, -14244248]\) \(1083523132511/50179392120\) \(-88895854083499320\) \([2]\) \(552960\) \(1.9320\)  
47190.h1 47190h4 \([1, 1, 0, -738828, -244742472]\) \(25176685646263969/57915000\) \(102599955315000\) \([2]\) \(552960\) \(1.9320\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.h

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