Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-144.4-d
Conductor 144.4
Rank \( 1 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 144.4-d over \(\Q(\sqrt{17}) \)

Isogeny class 144.4-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
144.4-d1 \( \bigl[a\) , \( a\) , \( 0\) , \( 741 a - 1903\) , \( -16047 a + 41078\bigr] \)
144.4-d2 \( \bigl[a\) , \( -1\) , \( 0\) , \( 6 a + 8\) , \( -33 a - 52\bigr] \)
144.4-d3 \( \bigl[a\) , \( 1\) , \( 0\) , \( -6 a - 8\) , \( 5 a + 8\bigr] \)
144.4-d4 \( \bigl[a\) , \( a\) , \( 0\) , \( 11 a - 23\) , \( 17 a - 42\bigr] \)
144.4-d5 \( \bigl[a\) , \( a\) , \( 0\) , \( 46 a - 123\) , \( -258 a + 634\bigr] \)
144.4-d6 \( \bigl[a\) , \( a\) , \( 0\) , \( -89 a + 57\) , \( -1329 a + 2254\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph