Elliptic curve isogeny class 12288.1-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12288.1-g
• Conductor: 12288.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 12288.1-g over \(\Q(\sqrt{-3}) \)

Isogeny class 12288.1-g contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
12288.1-g1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 20 a + 23\) , \( -68 a + 103\bigr] \)
12288.1-g2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20 a + 43\) , \( 68 a + 35\bigr] \)
12288.1-g3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 63\) , \( -1377\bigr] \)
12288.1-g4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \)
12288.1-g5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -17\) , \( 15\bigr] \)
12288.1-g6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -97\) , \( -385\bigr] \)
12288.1-g7	\( \bigl[0\) , \( 1\) , \( 0\) , \( -257\) , \( 1503\bigr] \)
12288.1-g8	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1537\) , \( -23713\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph