Elliptic curve isogeny class 8379.5-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-8379.5-a
• Conductor: 8379.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 8379.5-a over \(\Q(\sqrt{-3}) \)

Isogeny class 8379.5-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
8379.5-a1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -7912 a + 8171\) , \( -10322 a - 273673\bigr] \)
8379.5-a2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -6532 a + 2141\) , \( -171056 a + 165017\bigr] \)
8379.5-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -622 a + 476\) , \( -2951 a - 2080\bigr] \)
8379.5-a4	\( \bigl[a\) , \( -1\) , \( 0\) , \( 203 a - 109\) , \( -452 a - 316\bigr] \)
8379.5-a5	\( \bigl[a\) , \( -1\) , \( 0\) , \( 83 a - 64\) , \( 241 a - 43\bigr] \)
8379.5-a6	\( \bigl[a\) , \( -1\) , \( 0\) , \( 2948 a - 1414\) , \( -40205 a - 16444\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph