Elliptic curve isogeny class 8379.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-8379.2-a
• Conductor: 8379.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 8379.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 8379.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
8379.2-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 7912 a + 259\) , \( 10322 a - 283995\bigr] \)
8379.2-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 6532 a - 4391\) , \( 171056 a - 6039\bigr] \)
8379.2-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 622 a - 146\) , \( 2951 a - 5031\bigr] \)
8379.2-a4	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -203 a + 94\) , \( 452 a - 768\bigr] \)
8379.2-a5	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -83 a + 19\) , \( -241 a + 198\bigr] \)
8379.2-a6	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2948 a + 1534\) , \( 40205 a - 56649\bigr] \)

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