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Properties

Label 184093.h
Number of curves $2$
Conductor $184093$
CM no
Rank $1$
Graph

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

Elliptic curves in class 184093.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
184093.h1 184093h2 \([1, -1, 1, -165934173, -822678154336]\) \(177930109857804849/634933\) \(1803057879126131173\) \([2]\) \(24883200\) \(3.1447\)  
184093.h2 184093h1 \([1, -1, 1, -10375588, -12840160826]\) \(43499078731809/82055753\) \(233018715320006481593\) \([2]\) \(12441600\) \(2.7982\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 184093.h have rank \(1\).

Complex multiplication

The elliptic curves in class 184093.h do not have complex multiplication.

Modular form 184093.2.a.h

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