Elliptic curve isogeny class 2304.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-2304.1-b
• Conductor: 2304.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2304.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 2304.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
2304.1-b1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 32\) , \( 44 a - 48\bigr] \)
2304.1-b2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14 a - 17\) , \( 59 a + 21\bigr] \)
2304.1-b3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 47\) , \( -1033 a + 540\bigr] \)
2304.1-b4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( 2 a\bigr] \)
2304.1-b5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 13\) , \( 11 a - 12\bigr] \)
2304.1-b6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( -289 a + 108\bigr] \)
2304.1-b7	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 193\) , \( 1127 a - 660\bigr] \)
2304.1-b8	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1153\) , \( -17785 a + 8316\bigr] \)

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