Elliptic curve isogeny class 2268.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-2268.2-a
• Conductor: 2268.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 2268.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 2268.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
2268.2-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a - 3\) , \( 3 a\bigr] \)
2268.2-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a + 27\) , \( -63 a - 18\bigr] \)
2268.2-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a + 102\) , \( 465 a - 273\bigr] \)
2268.2-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a - 14\) , \( -6 a - 16\bigr] \)
2268.2-a5	\( \bigl[1\) , \( -1\) , \( 0\) , \( 303 a - 273\) , \( 2091 a - 762\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph