Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-32193.1-a
Conductor 32193.1
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 32193.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 32193.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
32193.1-a1 \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -262 a - 16\) , \( 1736 a - 716\bigr] \)
32193.1-a2 \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 128 a - 76\) , \( 494 a - 50\bigr] \)
32193.1-a3 \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 8 a - 1\) , \( 20 a - 11\bigr] \)
32193.1-a4 \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -307 a + 104\) , \( 2015 a + 598\bigr] \)

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