Elliptic curve isogeny class 8788.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-8788.2-a
• Number of curves: 5
• Conductor: 8788.2
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 9 & 9 & 9 \\ 3 & 1 & 3 & 3 & 3 \\ 9 & 3 & 1 & 9 & 9 \\ 9 & 3 & 9 & 1 & 9 \\ 9 & 3 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 8788.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 8788.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
8788.2-a1	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 6892 a - 3217\) , \( -137871 a - 65106\bigr] \)
8788.2-a2	\( \bigl[a\) , \( 1\) , \( 1\) , \( -32 a - 36\) , \( -279 a - 132\bigr] \)
8788.2-a3	\( \bigl[a\) , \( 1\) , \( 1\) , \( 3 a + 4\) , \( 9 a + 4\bigr] \)
8788.2-a4	\( \bigl[a\) , \( 1\) , \( 1\) , \( -2502 a + 2694\) , \( -6259 a - 47140\bigr] \)
8788.2-a5	\( \bigl[a\) , \( 1\) , \( 1\) , \( 2788 a - 2366\) , \( -56939 a + 17296\bigr] \)