Properties

Label 424830.g
Number of curves $2$
Conductor $424830$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 424830.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.g1 424830g2 \([1, 1, 0, -768023, 258745677]\) \(-12242088317612041/600\) \(-2455517400\) \([]\) \(2939328\) \(1.7255\) \(\Gamma_0(N)\)-optimal*
424830.g2 424830g1 \([1, 1, 0, -9398, 358002]\) \(-22434194041/843750\) \(-3453071343750\) \([]\) \(979776\) \(1.1762\) \(\Gamma_0(N)\)-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 424830.g1.

Rank

sage: E.rank()
 

The elliptic curves in class 424830.g have rank \(1\).

Complex multiplication

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

Modular form 424830.2.a.g

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.