Properties

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

Isogeny class 324.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
324.1-d1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a - 6\) , \( 7 a + 12\bigr] \)
324.1-d2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a + 39\) , \( -81 a - 127\bigr] \)
324.1-d3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a + 66\) , \( 81 a - 208\bigr] \)
324.1-d4 \( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a - 9\) , \( -7 a + 19\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph