Properties

Label 476850.gj
Number of curves $2$
Conductor $476850$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 476850.gj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
476850.gj1 476850gj2 [1, 1, 1, -1036938, 259175781] [2] 14155776 \(\Gamma_0(N)\)-optimal*
476850.gj2 476850gj1 [1, 1, 1, 191312, 28264781] [2] 7077888 \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 476850.gj1.

Rank

sage: E.rank()
 

The elliptic curves in class 476850.gj have rank \(0\).

Complex multiplication

The elliptic curves in class 476850.gj do not have complex multiplication.

Modular form 476850.2.a.gj

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} - q^{11} - q^{12} - 2q^{14} + q^{16} + q^{18} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.