Properties

Label 424830w
Number of curves $2$
Conductor $424830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 424830w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.w2 424830w1 \([1, 1, 0, -37859728, -116141589248]\) \(-2113364608155289/828431400960\) \(-2352547063731806644469760\) \([2]\) \(104509440\) \(3.3856\) \(\Gamma_0(N)\)-optimal*
424830.w1 424830w2 \([1, 1, 0, -654146448, -6439366593792]\) \(10901014250685308569/1040774054400\) \(2955549418877218021286400\) \([2]\) \(209018880\) \(3.7322\) \(\Gamma_0(N)\)-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 424830w1.

Rank

sage: E.rank()
 

The elliptic curves in class 424830w have rank \(0\).

Complex multiplication

The elliptic curves in class 424830w do not have complex multiplication.

Modular form 424830.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} - 4 q^{13} + q^{15} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.