Properties

Base field \(\Q(\sqrt{22}) \)
Label 2.2.88.1-72.1-d
Conductor 72.1
Rank not recorded

Related objects

Learn more about

Base field \(\Q(\sqrt{22}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 22 \); class number \(1\).

Elliptic curves in class 72.1-d over \(\Q(\sqrt{22}) \)

Isogeny class 72.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
72.1-d1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -64813 a + 304014\) , \( 142270436 a - 667307485\bigr] \)
72.1-d2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-d3 \( \bigl[a\) , \( 1\) , \( 0\) , \( 17927 a - 84071\) , \( -2074079 a + 9728303\bigr] \)
72.1-d4 \( \bigl[a\) , \( 1\) , \( 0\) , \( 100667 a - 472156\) , \( 36137766 a - 169501137\bigr] \)
72.1-d5 \( \bigl[a\) , \( 1\) , \( 0\) , \( -266147 a - 1248326\) , \( 161273084 a + 756437825\bigr] \)
72.1-d6 \( \bigl[a\) , \( 1\) , \( 0\) , \( 1589987 a - 7457686\) , \( 2366958216 a - 11102018109\bigr] \)

Rank

Rank not yet determined.

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