Properties

Label 47190k
Number of curves $6$
Conductor $47190$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("47190.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47190.n6 47190k1 [1, 1, 0, 1813, -11139] [2] 81920 \(\Gamma_0(N)\)-optimal
47190.n5 47190k2 [1, 1, 0, -7867, -102131] [2, 2] 163840  
47190.n3 47190k3 [1, 1, 0, -68367, 6782769] [2, 2] 327680  
47190.n2 47190k4 [1, 1, 0, -102247, -12616919] [2] 327680  
47190.n4 47190k5 [1, 1, 0, -13917, 17356959] [2] 655360  
47190.n1 47190k6 [1, 1, 0, -1090817, 438052179] [2] 655360  

Rank

sage: E.rank()
 

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

Modular form 47190.2.a.n

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.