Properties

Label 436800.h
Number of curves $2$
Conductor $436800$
CM no
Rank $2$
Graph

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

Elliptic curves in class 436800.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.h1 436800h1 \([0, -1, 0, -7952833, -8530306463]\) \(108647414150813/1440074181\) \(737317980672000000000\) \([2]\) \(24576000\) \(2.8114\) \(\Gamma_0(N)\)-optimal
436800.h2 436800h2 \([0, -1, 0, -1192833, -22570826463]\) \(-366600498893/429644853729\) \(-219978165109248000000000\) \([2]\) \(49152000\) \(3.1580\)  

Rank

sage: E.rank()
 

The elliptic curves in class 436800.h have rank \(2\).

Complex multiplication

The elliptic curves in class 436800.h do not have complex multiplication.

Modular form 436800.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 6 q^{11} + q^{13} + 2 q^{19} + O(q^{20})\) 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.