Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-192.1-e
Conductor 192.1
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 192.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 192.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
192.1-e1 \( \bigl[0\) , \( -a\) , \( 0\) , \( -78 a + 221\) , \( -4241 a + 11838\bigr] \)
192.1-e2 \( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 11\) , \( 4 a - 12\bigr] \)
192.1-e3 \( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 59\) , \( 75 a - 210\bigr] \)
192.1-e4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -122 a - 217\) , \( 985 a + 1765\bigr] \)
192.1-e5 \( \bigl[0\) , \( -a\) , \( 0\) , \( 322 a - 899\) , \( 4959 a - 13842\bigr] \)
192.1-e6 \( \bigl[0\) , \( -a\) , \( 0\) , \( 1922 a - 5379\) , \( -68449 a + 191102\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph