Elliptic curve isogeny class 8281.8-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-8281.8-a
• Conductor: 8281.8
• Rank: \( 1 \)

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

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

Elliptic curves in class 8281.8-a over \(\Q(\sqrt{-3}) \)

Isogeny class 8281.8-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
8281.8-a1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 24 a - 25\) , \( -47 a + 25\bigr] \)
8281.8-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 7 a - 27\) , \( 21 a - 46\bigr] \)
8281.8-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 47 a - 42\) , \( -149 a - 19\bigr] \)
8281.8-a4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 9 a - 50\) , \( -37 a - 138\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph