Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-16.1-b
Conductor 16.1
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 16.1-b over \(\Q(\sqrt{19}) \)

Isogeny class 16.1-b contains 2 curves linked by isogenies of degree 19.

Curve label Weierstrass Coefficients
16.1-b1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -8\) , \( -2 a\bigr] \)
16.1-b2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -8\) , \( 2 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph