Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-32.4-a
Conductor 32.4
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 32.4-a over \(\Q(\sqrt{17}) \)

Isogeny class 32.4-a contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
32.4-a1 \( \bigl[a\) , \( -1\) , \( a\) , \( -23 a + 52\) , \( -405 a + 1032\bigr] \)
32.4-a2 \( \bigl[a\) , \( -1\) , \( a\) , \( -7 a - 12\) , \( 67 a + 104\bigr] \)
32.4-a3 \( \bigl[a\) , \( -1\) , \( a\) , \( 58 a + 88\) , \( -1783 a - 2784\bigr] \)
32.4-a4 \( \bigl[a\) , \( -1\) , \( a\) , \( 2 a - 8\) , \( 15 a - 40\bigr] \)
32.4-a5 \( \bigl[a\) , \( 1\) , \( a\) , \( -7 a - 12\) , \( -7 a - 12\bigr] \)
32.4-a6 \( \bigl[a\) , \( a\) , \( a\) , \( 2388 a - 6147\) , \( -92365 a + 236610\bigr] \)
32.4-a7 \( \bigl[a\) , \( a\) , \( a\) , \( 148 a - 387\) , \( -1485 a + 3778\bigr] \)
32.4-a8 \( \bigl[a\) , \( a\) , \( a\) , \( 3 a - 7\) , \( -a + 2\bigr] \)
32.4-a9 \( \bigl[a\) , \( 1\) , \( a\) , \( -77 a - 132\) , \( -619 a - 988\bigr] \)
32.4-a10 \( \bigl[a\) , \( 1\) , \( a\) , \( -402 a - 632\) , \( -6673 a - 10420\bigr] \)
32.4-a11 \( \bigl[a\) , \( a\) , \( a\) , \( 23 a - 87\) , \( -129 a + 354\bigr] \)
32.4-a12 \( \bigl[a\) , \( 1\) , \( a\) , \( -6442 a - 10072\) , \( -410033 a - 640308\bigr] \)

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