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Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 424830.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.h1 424830h2 \([1, 1, 0, -533636338, 4738656424468]\) \(5918043195362419129/8515734343200\) \(24182649041791416786439200\) \([2]\) \(212336640\) \(3.7731\) \(\Gamma_0(N)\)-optimal*
424830.h2 424830h1 \([1, 1, 0, -23840338, 117151766068]\) \(-527690404915129/1782829440000\) \(-5062809255354546272640000\) \([2]\) \(106168320\) \(3.4265\) \(\Gamma_0(N)\)-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.h1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 424830.2.a.h

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