Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1024.1-r
Conductor 1024.1
Rank not recorded

Related objects

Learn more about

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 1024.1-r over \(\Q(\sqrt{3}) \)

Isogeny class 1024.1-r contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1024.1-r1 \( \bigl[0\) , \( a\) , \( 0\) , \( 118 a - 203\) , \( 849 a - 1470\bigr] \)
1024.1-r2 \( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 13\) , \( 7 a - 12\bigr] \)
1024.1-r3 \( \bigl[0\) , \( a\) , \( 0\) , \( -2\) , \( -2 a\bigr] \)
1024.1-r4 \( \bigl[0\) , \( a\) , \( 0\) , \( -22 a + 37\) , \( 89 a - 154\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph