Elliptic curve isogeny class 8281.5-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-8281.5-a
• Conductor: 8281.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 8281.5-a over \(\Q(\sqrt{-3}) \)

Isogeny class 8281.5-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
8281.5-a1	\( \bigl[0\) , \( -a\) , \( 1\) , \( -7 a + 7\) , \( 5\bigr] \)
8281.5-a2	\( \bigl[0\) , \( -a\) , \( 1\) , \( -117 a + 117\) , \( -1245\bigr] \)
8281.5-a3	\( \bigl[0\) , \( -a\) , \( 1\) , \( 13 a - 13\) , \( 42\bigr] \)
8281.5-a4	\( \bigl[0\) , \( -a\) , \( 1\) , \( 503 a - 1273\) , \( -9086 a + 16555\bigr] \)
8281.5-a5	\( \bigl[0\) , \( -a\) , \( 1\) , \( 1273 a - 503\) , \( 9086 a + 7469\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 3 & 9 & 9 \\ 9 & 1 & 3 & 9 & 9 \\ 3 & 3 & 1 & 3 & 3 \\ 9 & 9 & 3 & 1 & 9 \\ 9 & 9 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph