Elliptic curve isogeny class 32193.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-32193.2-b
• Conductor: 32193.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 32193.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 32193.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
32193.2-b1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -103 a - 205\) , \( -1178 a - 1036\bigr] \)
32193.2-b2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -43 a + 125\) , \( -416 a + 68\bigr] \)
32193.2-b3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 17 a - 280\) , \( -2657 a + 17\bigr] \)
32193.2-b4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 5\) , \( -2 a - 7\bigr] \)

Rank

Rank: \( 0 \)

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