Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-5324.6-d
Conductor 5324.6
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 5324.6-d over \(\Q(\sqrt{-7}) \)

Isogeny class 5324.6-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
5324.6-d1 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -48 a - 272\) , \( -3251 a + 4009\bigr] \)
5324.6-d2 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -158 a + 297\) , \( -3796 a + 3141\bigr] \)
5324.6-d3 \( \bigl[1\) , \( a\) , \( 0\) , \( -307 a - 542\) , \( -4407 a - 3414\bigr] \)
5324.6-d4 \( \bigl[1\) , \( 0\) , \( a\) , \( -538 a + 647\) , \( -193 a + 7937\bigr] \)
5324.6-d5 \( \bigl[1\) , \( a\) , \( 0\) , \( -4707 a - 8462\) , \( -291111 a - 234502\bigr] \)
5324.6-d6 \( \bigl[1\) , \( 0\) , \( a\) , \( -8298 a + 10087\) , \( -17537 a + 545409\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph