Properties

Label 479808ny
Number of curves $4$
Conductor $479808$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ny1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 479808ny

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479808.ny4 479808ny1 \([0, 0, 0, 27636, -477812720]\) \(103823/4386816\) \(-98629108855140777984\) \([2]\) \(14155776\) \(2.5154\) \(\Gamma_0(N)\)-optimal*
479808.ny3 479808ny2 \([0, 0, 0, -9004044, -10213963760]\) \(3590714269297/73410624\) \(1650496493497746456576\) \([2, 2]\) \(28311552\) \(2.8620\) \(\Gamma_0(N)\)-optimal*
479808.ny2 479808ny3 \([0, 0, 0, -19164684, 17069386768]\) \(34623662831857/14438442312\) \(324620567283633160716288\) \([2]\) \(56623104\) \(3.2085\) \(\Gamma_0(N)\)-optimal*
479808.ny1 479808ny4 \([0, 0, 0, -143350284, -660610980848]\) \(14489843500598257/6246072\) \(140430899131635990528\) \([2]\) \(56623104\) \(3.2085\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 479808ny1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 479808.2.a.ny

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.