Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-1024.6-b
Conductor 1024.6
Rank \( 0 \)

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 1024.6-b over \(\Q(\sqrt{-7}) \)

Isogeny class 1024.6-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1024.6-b1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \)
1024.6-b2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 5\) , \( 3 a + 5\bigr] \)
1024.6-b3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a\) , \( 8 a - 8\bigr] \)
1024.6-b4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 10\) , \( 6 a - 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph