Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-32193.5-b
Conductor 32193.5
Rank not recorded

Related objects

Learn more about

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

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

Elliptic curves in class 32193.5-b over \(\Q(\sqrt{-3}) \)

Isogeny class 32193.5-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
32193.5-b1 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -309 a + 204\) , \( 869 a - 2009\bigr] \)
32193.5-b2 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 81 a - 126\) , \( 497 a - 473\bigr] \)
32193.5-b3 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 6 a - 6\) , \( 8 a - 14\bigr] \)
32193.5-b4 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -264 a + 279\) , \( 2393 a - 2360\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph