Elliptic curve isogeny class 399.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-399.3-a
• Conductor: 399.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 399.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 399.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
399.3-a1	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 152 a - 436\) , \( -1813 a + 3394\bigr] \)
399.3-a2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 282 a - 266\) , \( 1961 a - 886\bigr] \)
399.3-a3	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 17 a - 31\) , \( -4 a + 46\bigr] \)
399.3-a4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -8 a + 9\) , \( 2 a + 7\bigr] \)
399.3-a5	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -3 a + 4\) , \( -a - 1\bigr] \)
399.3-a6	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -113 a + 129\) , \( 140 a + 460\bigr] \)

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