Elliptic curve isogeny class 32193.6-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-32193.6-a
• Conductor: 32193.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 32193.6-a over \(\Q(\sqrt{-3}) \)

Isogeny class 32193.6-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
32193.6-a1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -280 a + 16\) , \( -2015 a + 1036\bigr] \)
32193.6-a2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 50 a + 76\) , \( -443 a + 520\bigr] \)
32193.6-a3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -205 a - 104\) , \( -2219 a + 2509\bigr] \)
32193.6-a4	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 5 a + 1\) , \( -14 a + 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph