Properties

Label 476850ea
Number of curves 2
Conductor 476850
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("476850.ea1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 476850ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
476850.ea2 476850ea1 [1, 0, 1, -6358151, 2717178698] [u'2'] 37158912 \(\Gamma_0(N)\)-optimal*
476850.ea1 476850ea2 [1, 0, 1, -84966151, 301270362698] [u'2'] 74317824 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 476850ea1.

Rank

sage: E.rank()
 

The elliptic curves in class 476850ea have rank \(1\).

Modular form 476850.2.a.ea

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + 4q^{13} + 2q^{14} + q^{16} - q^{18} - 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.