Properties

Label 47432g
Number of curves $4$
Conductor $47432$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47432g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47432.n4 47432g1 [0, 0, 0, 5929, 913066] [2] 122880 \(\Gamma_0(N)\)-optimal
47432.n3 47432g2 [0, 0, 0, -112651, 13695990] [2, 2] 245760  
47432.n2 47432g3 [0, 0, 0, -349811, -63001554] [2] 491520  
47432.n1 47432g4 [0, 0, 0, -1772771, 908500670] [2] 491520  

Rank

sage: E.rank()
 

The elliptic curves in class 47432g have rank \(1\).

Complex multiplication

The elliptic curves in class 47432g do not have complex multiplication.

Modular form 47432.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.