Elliptic curve isogeny class 768.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-768.1-a
• Conductor: 768.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 768.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 768.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
768.1-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 6\) , \( -11 a + 1\bigr] \)
768.1-a2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 11\) , \( 11 a - 10\bigr] \)
768.1-a3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 16\) , \( 180\bigr] \)
768.1-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 1\) , \( 0\bigr] \)
768.1-a5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -4 a + 4\) , \( -4\bigr] \)
768.1-a6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -24 a + 24\) , \( 36\bigr] \)
768.1-a7	\( \bigl[0\) , \( -a\) , \( 0\) , \( -64 a + 64\) , \( -220\bigr] \)
768.1-a8	\( \bigl[0\) , \( -a\) , \( 0\) , \( -384 a + 384\) , \( 2772\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 2 & 4 & 8 & 8 & 16 \\ 4 & 1 & 16 & 2 & 4 & 8 & 8 & 16 \\ 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 \\ 2 & 2 & 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 8 & 8 & 4 & 2 & 4 & 1 & 8 \\ 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph