Elliptic curve isogeny class 2268.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-2268.1-a
• Conductor: 2268.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2268.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 2268.1-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
2268.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a\) , \( -3 a + 3\bigr] \)
2268.1-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a\) , \( 63 a - 81\bigr] \)
2268.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a + 105\) , \( -465 a + 192\bigr] \)
2268.1-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a - 17\) , \( 6 a - 22\bigr] \)
2268.1-a5	\( \bigl[1\) , \( -1\) , \( 0\) , \( -303 a + 30\) , \( -2091 a + 1329\bigr] \)

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