Elliptic curve isogeny class 1083.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-1083.2-b
• Conductor: 1083.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1083.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 1083.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1083.2-b1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 130 a + 63\) , \( -464 a + 999\bigr] \)
1083.2-b2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a + 193\) , \( 464 a + 535\bigr] \)
1083.2-b3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \)
1083.2-b4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \)
1083.2-b5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \)
1083.2-b6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 8 & 4 & 8 \\ 4 & 1 & 2 & 8 & 4 & 8 \\ 2 & 2 & 1 & 4 & 2 & 4 \\ 8 & 8 & 4 & 1 & 2 & 4 \\ 4 & 4 & 2 & 2 & 1 & 2 \\ 8 & 8 & 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph