Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-324.1-e
Conductor 324.1
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 324.1-e over \(\Q(\sqrt{17}) \)

Isogeny class 324.1-e contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
324.1-e1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -81 a + 202\) , \( -2862 a + 7337\bigr] \)
324.1-e2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -9 a - 14\) , \( -108 a - 169\bigr] \)
324.1-e3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 81 a + 121\) , \( 2862 a + 4475\bigr] \)
324.1-e4 \( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 23\) , \( 108 a - 277\bigr] \)
324.1-e5 \( \bigl[1\) , \( -1\) , \( 1\) , \( -9 a - 17\) , \( 4 a + 5\bigr] \)
324.1-e6 \( \bigl[1\) , \( -1\) , \( 1\) , \( 8829 a - 22661\) , \( -651802 a + 1669545\bigr] \)
324.1-e7 \( \bigl[1\) , \( -1\) , \( 1\) , \( 549 a - 1421\) , \( -10282 a + 26361\bigr] \)
324.1-e8 \( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 26\) , \( -4 a + 9\bigr] \)
324.1-e9 \( \bigl[1\) , \( -1\) , \( 1\) , \( -99 a - 197\) , \( 940 a + 1373\bigr] \)
324.1-e10 \( \bigl[1\) , \( -1\) , \( 1\) , \( -549 a - 872\) , \( 10282 a + 16079\bigr] \)
324.1-e11 \( \bigl[1\) , \( -1\) , \( 1\) , \( 99 a - 296\) , \( -940 a + 2313\bigr] \)
324.1-e12 \( \bigl[1\) , \( -1\) , \( 1\) , \( -8829 a - 13832\) , \( 651802 a + 1017743\bigr] \)

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