Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-68.1-a
Conductor 68.1
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 68.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 68.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
68.1-a1 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -611 a - 955\) , \( -16227 a - 25345\bigr] \)
68.1-a2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 50 a - 128\) , \( 290 a - 743\bigr] \)
68.1-a3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( 1\bigr] \)
68.1-a4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -113\) , \( -329\bigr] \)
68.1-a5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -50 a - 78\) , \( -290 a - 453\bigr] \)
68.1-a6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -43\) , \( 105\bigr] \)
68.1-a7 \( \bigl[1\) , \( 0\) , \( 0\) , \( -103\) , \( -411\bigr] \)
68.1-a8 \( \bigl[1\) , \( a\) , \( a\) , \( 610 a - 1565\) , \( 16226 a - 41571\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph