Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 424830u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
424830.u2 424830u1 [1, 1, 0, 6659443612, -2754863188541232] [2] 2972712960 \(\Gamma_0(N)\)-optimal*
424830.u1 424830u2 [1, 1, 0, -258859306388, -49006795637291232] [2] 5945425920 \(\Gamma_0(N)\)-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 424830u1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 424830.2.a.u

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

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.