Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 424830.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.e1 424830e2 \([1, 1, 0, -10000043, -12173472303]\) \(557827933667759/126562500\) \(25091935885110937500\) \([2]\) \(29360128\) \(2.7145\) \(\Gamma_0(N)\)-optimal*
424830.e2 424830e1 \([1, 1, 0, -553823, -235339467]\) \(-94756448879/65610000\) \(-13007659562841510000\) \([2]\) \(14680064\) \(2.3679\) \(\Gamma_0(N)\)-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.e1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 424830.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.