Elliptic curve isogeny class 324.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-324.1-a
• Conductor: 324.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 324.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 324.1-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
324.1-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 91 a - 62\) , \( -276 a - 13\bigr] \)
324.1-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 61 a - 92\) , \( 276 a - 289\bigr] \)
324.1-a3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( 3\bigr] \)
324.1-a4	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -14 a + 13\) , \( 29\bigr] \)
324.1-a5	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( a - 2\) , \( -1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph