Elliptic curve isogeny class 9408.2-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-9408.2-f
• Conductor: 9408.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 9408.2-f over \(\Q(\sqrt{-3}) \)

Isogeny class 9408.2-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9408.2-f1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 48 a - 48\) , \( 48\bigr] \)
9408.2-f2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a + 12\) , \( 0\bigr] \)
9408.2-f3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -7 a + 7\) , \( -10\bigr] \)
9408.2-f4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 568 a - 488\) , \( 5312 a - 1552\bigr] \)
9408.2-f5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 488 a - 568\) , \( -5312 a + 3760\bigr] \)
9408.2-f6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -152 a + 152\) , \( 672\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 2 & 2 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 8 & 8 & 4 \\ 2 & 4 & 8 & 1 & 4 & 8 \\ 2 & 4 & 8 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph