Elliptic curve isogeny class 12675.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12675.2-b
• Conductor: 12675.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 12675.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 12675.2-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
12675.2-b1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -7930 a + 7930\) , \( -296725\bigr] \)
12675.2-b2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 605 a - 605\) , \( -19750\bigr] \)
12675.2-b3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 210 a - 210\) , \( 2277\bigr] \)
12675.2-b4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -115 a + 115\) , \( 392\bigr] \)
12675.2-b5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -520 a + 520\) , \( -4225\bigr] \)
12675.2-b6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -110 a + 110\) , \( 435\bigr] \)
12675.2-b7	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -8125 a + 8125\) , \( -282568\bigr] \)
12675.2-b8	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -130000 a + 130000\) , \( -18051943\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph