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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-9408.2-e
• Conductor: 9408.2
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
9408.2-e1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \)
9408.2-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -392\) , \( -228\bigr] \)
9408.2-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -195 a + 158\) , \( -243 a + 970\bigr] \)
9408.2-e4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 195 a - 37\) , \( 243 a + 727\bigr] \)
9408.2-e5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -252\) , \( 1620\bigr] \)
9408.2-e6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4032\) , \( 99900\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph