Properties

Label 479808os
Number of curves $2$
Conductor $479808$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("os1")
 
E.isogeny_class()
 

Elliptic curves in class 479808os

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479808.os2 479808os1 \([0, 0, 0, -607404, -255548720]\) \(-1102302937/616896\) \(-13869718432754171904\) \([2]\) \(7077888\) \(2.3763\) \(\Gamma_0(N)\)-optimal*
479808.os1 479808os2 \([0, 0, 0, -10768044, -13598501168]\) \(6141556990297/1019592\) \(22923562409690923008\) \([2]\) \(14155776\) \(2.7229\) \(\Gamma_0(N)\)-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 479808os1.

Rank

sage: E.rank()
 

The elliptic curves in class 479808os have rank \(1\).

Complex multiplication

The elliptic curves in class 479808os do not have complex multiplication.

Modular form 479808.2.a.os

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + 2 q^{11} + 4 q^{13} + q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.