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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-8379.5-d
• 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-d over \(\Q(\sqrt{-3}) \)

Isogeny class 8379.5-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
8379.5-d1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 19 a - 17\) , \( 46 a - 16\bigr] \)
8379.5-d2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -36 a - 27\) , \( 183 a + 49\bigr] \)
8379.5-d3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 15 a\) , \( 12 a - 16\bigr] \)
8379.5-d4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 180 a + 30\) , \( 297 a - 1207\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph