Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-576.7-e
Conductor 576.7
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 576.7-e over \(\Q(\sqrt{17}) \)

Isogeny class 576.7-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
576.7-e1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -101 a - 157\) , \( -1084 a - 1693\bigr] \)
576.7-e2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 974 a - 2497\) , \( 24826 a - 63589\bigr] \)
576.7-e3 \( \bigl[a\) , \( 0\) , \( a\) , \( 120 a + 188\) , \( -1029 a - 1608\bigr] \)
576.7-e4 \( \bigl[a\) , \( 0\) , \( a\) , \( -45 a - 72\) , \( -189 a - 296\bigr] \)
576.7-e5 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 59 a - 157\) , \( 436 a - 1117\bigr] \)
576.7-e6 \( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 29\) , \( -34 a + 35\bigr] \)
576.7-e7 \( \bigl[a\) , \( -a\) , \( 0\) , \( -100 a - 156\) , \( 813 a + 1268\bigr] \)
576.7-e8 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -68 a - 89\) , \( -604 a - 613\bigr] \)

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