Properties

Label 474320bj
Number of curves 4
Conductor 474320
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("474320.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 474320bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
474320.bj3 474320bj1 [0, 1, 0, -5314360, -91766155692] [u'2'] 79626240 \(\Gamma_0(N)\)-optimal*
474320.bj2 474320bj2 [0, 1, 0, -339235640, -2383668253100] [u'2'] 159252480 \(\Gamma_0(N)\)-optimal*
474320.bj4 474320bj3 [0, 1, 0, 47809480, 2471926614100] [u'2'] 238878720 \(\Gamma_0(N)\)-optimal*
474320.bj1 474320bj4 [0, 1, 0, -2477470200, 46117850491348] [u'2'] 477757440 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 474320bj1.

Rank

sage: E.rank()
 

The elliptic curves in class 474320bj have rank \(1\).

Modular form 474320.2.a.bj

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.