Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-8.3-a
Conductor 8.3
Rank not recorded

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

Isogeny class 8.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
8.3-a1 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4 a + 7\) , \( -34 a - 53\bigr] \)
8.3-a2 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 80 a + 125\) , \( 1186 a + 1852\bigr] \)
8.3-a3 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 12 a - 37\) , \( 46 a - 121\bigr] \)
8.3-a4 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( a + 3\) , \( 0\bigr] \)
8.3-a5 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a - 8\) , \( 2 a + 3\bigr] \)
8.3-a6 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 12\) , \( -29 a - 31\bigr] \)

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