Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-17.1-a
Conductor 17.1
Rank not recorded

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 17.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 17.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
17.1-a1 \( \bigl[1\) , \( -1\) , \( 1\) , \( 330 a - 936\) , \( 4996 a - 13110\bigr] \)
17.1-a2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \)
17.1-a3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a + 9\) , \( 4 a + 6\bigr] \)
17.1-a4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
17.1-a5 \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
17.1-a6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 15\) , \( -4 a + 10\bigr] \)
17.1-a7 \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)
17.1-a8 \( \bigl[1\) , \( -1\) , \( 1\) , \( -330 a - 606\) , \( -4996 a - 8114\bigr] \)

Rank

Rank not yet determined.

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