Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-576.6-e
Conductor 576.6
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 576.6-e over \(\Q(\sqrt{17}) \)

Isogeny class 576.6-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
576.6-e1 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 100 a - 256\) , \( -813 a + 2081\bigr] \)
576.6-e2 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 71 a - 156\) , \( 446 a - 779\bigr] \)
576.6-e3 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -122 a + 308\) , \( 1028 a - 2637\bigr] \)
576.6-e4 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 43 a - 117\) , \( 188 a - 485\bigr] \)
576.6-e5 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 21\) , \( 11 a + 4\bigr] \)
576.6-e6 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -61 a - 98\) , \( -437 a - 681\bigr] \)
576.6-e7 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 99 a - 258\) , \( 1083 a - 2777\bigr] \)
576.6-e8 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -976 a - 1523\) , \( -24827 a - 38763\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph