Properties

Label 16762.h
Number of curves $2$
Conductor $16762$
CM no
Rank $1$
Graph

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

Elliptic curves in class 16762.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16762.h1 16762i2 \([1, 0, 0, -131501, -18489883]\) \(-10418796526321/82044596\) \(-1980357097027124\) \([]\) \(83200\) \(1.7638\)  
16762.h2 16762i1 \([1, 0, 0, 1439, 35017]\) \(13651919/29696\) \(-716789249024\) \([]\) \(16640\) \(0.95905\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16762.h have rank \(1\).

Complex multiplication

The elliptic curves in class 16762.h do not have complex multiplication.

Modular form 16762.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} + q^{8} - 2 q^{9} - q^{10} + 3 q^{11} + q^{12} - q^{13} + 2 q^{14} - q^{15} + q^{16} - 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.