Elliptic curve isogeny class 399.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-399.2-a
• Conductor: 399.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 399.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 399.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
399.2-a1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -153 a - 284\) , \( 1812 a + 1581\bigr] \)
399.2-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -283 a + 16\) , \( -1962 a + 1075\bigr] \)
399.2-a3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -18 a - 14\) , \( 3 a + 42\bigr] \)
399.2-a4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 7 a + 1\) , \( -3 a + 9\bigr] \)
399.2-a5	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 2 a + 1\) , \( -2\bigr] \)
399.2-a6	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 112 a + 16\) , \( -141 a + 600\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph