Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-16.5-a
Conductor 16.5
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 16.5-a over \(\Q(\sqrt{17}) \)

Isogeny class 16.5-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
16.5-a1 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \)
16.5-a2 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 7 a - 2\) , \( 5 a - 5\bigr] \)
16.5-a3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \)
16.5-a4 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 12 a - 22\) , \( -7 a + 26\bigr] \)
16.5-a5 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 4\) , \( 5 a - 16\bigr] \)
16.5-a6 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 127 a - 317\) , \( -1109 a + 2848\bigr] \)

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