Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-324.1-a
Conductor 324.1
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 324.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 324.1-a contains 8 curves linked by isogenies of degrees dividing 20.

Curve label Weierstrass Coefficients
324.1-a1 \( \bigl[1\) , \( -1\) , \( 0\) , \( 17223 a - 45792\) , \( -1827113 a + 4707820\bigr] \)
324.1-a2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 33 a - 72\) , \( -131 a + 244\bigr] \)
324.1-a3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -33 a - 39\) , \( 131 a + 113\bigr] \)
324.1-a4 \( \bigl[1\) , \( -1\) , \( 0\) , \( 1563 a - 4005\) , \( 45119 a - 115575\bigr] \)
324.1-a5 \( \bigl[1\) , \( -1\) , \( 0\) , \( 178683 a - 457875\) , \( -57387877 a + 147002943\bigr] \)
324.1-a6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -24603 a - 38442\) , \( -3010943 a - 4701784\bigr] \)
324.1-a7 \( \bigl[1\) , \( -1\) , \( 0\) , \( -177243 a - 276942\) , \( 58383673 a + 91170068\bigr] \)
324.1-a8 \( \bigl[1\) , \( -1\) , \( 0\) , \( -17223 a - 28569\) , \( 1827113 a + 2880707\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 20 & 10 & 4 & 20 & 2 & 4 \\ 5 & 1 & 4 & 2 & 20 & 4 & 10 & 20 \\ 20 & 4 & 1 & 2 & 20 & 4 & 10 & 5 \\ 10 & 2 & 2 & 1 & 10 & 2 & 5 & 10 \\ 4 & 20 & 20 & 10 & 1 & 5 & 2 & 4 \\ 20 & 4 & 4 & 2 & 5 & 1 & 10 & 20 \\ 2 & 10 & 10 & 5 & 2 & 10 & 1 & 2 \\ 4 & 20 & 5 & 10 & 4 & 20 & 2 & 1 \end{array}\right)\)

Isogeny graph