Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-289.1-a
Conductor 289.1
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 289.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 289.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
289.1-a1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -24497 a - 38627\) , \( -3044003 a - 4756060\bigr] \)
289.1-a2 \( \bigl[1\) , \( -1\) , \( 0\) , \( -187 a - 292\) , \( -126667 a - 197799\bigr] \)
289.1-a3 \( \bigl[1\) , \( -1\) , \( 0\) , \( 17 a - 37\) , \( -51 a + 132\bigr] \)
289.1-a4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -187 a - 292\) , \( 901 a + 1407\bigr] \)
289.1-a5 \( \bigl[1\) , \( -1\) , \( 0\) , \( -1547 a - 2417\) , \( -46597 a - 72764\bigr] \)
289.1-a6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -17 a - 20\) , \( 51 a + 81\bigr] \)
289.1-a7 \( \bigl[1\) , \( -1\) , \( 0\) , \( -24667 a - 38542\) , \( -3022719 a - 4720173\bigr] \)
289.1-a8 \( \bigl[1\) , \( -1\) , \( 0\) , \( 24497 a - 63124\) , \( 3044003 a - 7800063\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph