Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-32.3-a
Conductor 32.3
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 32.3-a over \(\Q(\sqrt{17}) \)

Isogeny class 32.3-a contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
32.3-a1 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -60 a + 146\) , \( 1782 a - 4567\bigr] \)
32.3-a2 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 6\) , \( -16 a - 25\bigr] \)
32.3-a3 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 21 a + 29\) , \( 404 a + 627\bigr] \)
32.3-a4 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 5 a - 19\) , \( -68 a + 171\bigr] \)
32.3-a5 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2\) , \( -4 a - 5\bigr] \)
32.3-a6 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 6440 a - 16514\) , \( 410032 a - 1050341\bigr] \)
32.3-a7 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 400 a - 1034\) , \( 6672 a - 17093\bigr] \)
32.3-a8 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 5 a - 19\) , \( 6 a - 19\bigr] \)
32.3-a9 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -20 a - 62\) , \( 44 a + 139\bigr] \)
32.3-a10 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -145 a - 237\) , \( 1100 a + 1707\bigr] \)
32.3-a11 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 75 a - 209\) , \( 618 a - 1607\bigr] \)
32.3-a12 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2385 a - 3757\) , \( 86220 a + 134699\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\ 24 & 1 & 3 & 8 & 4 & 12 & 6 & 2 & 8 & 12 & 4 & 24 \\ 8 & 3 & 1 & 24 & 12 & 4 & 2 & 6 & 24 & 4 & 12 & 8 \\ 3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\ 6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\ 8 & 12 & 4 & 24 & 12 & 1 & 2 & 6 & 24 & 4 & 3 & 8 \\ 4 & 6 & 2 & 12 & 6 & 2 & 1 & 3 & 12 & 2 & 6 & 4 \\ 12 & 2 & 6 & 4 & 2 & 6 & 3 & 1 & 4 & 6 & 2 & 12 \\ 12 & 8 & 24 & 4 & 2 & 24 & 12 & 4 & 1 & 6 & 8 & 3 \\ 2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\ 24 & 4 & 12 & 8 & 4 & 3 & 6 & 2 & 8 & 12 & 1 & 24 \\ 4 & 24 & 8 & 12 & 6 & 8 & 4 & 12 & 3 & 2 & 24 & 1 \end{array}\right)\)

Isogeny graph