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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-768.1-g
• Conductor: 768.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

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

Isogeny class 768.1-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
768.1-g1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 20 a - 34\) , \( -54 a + 104\bigr] \)
768.1-g2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -5980 a + 10358\) , \( 217250 a - 376288\bigr] \)
768.1-g3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1820 a - 3152\) , \( 30640 a - 53070\bigr] \)
768.1-g4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 242 a - 419\) , \( -2437 a + 4221\bigr] \)
768.1-g5	\( \bigl[0\) , \( 1\) , \( 0\) , \( 25220 a - 43682\) , \( 2876590 a - 4982400\bigr] \)
768.1-g6	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a + 31\) , \( -8073 a + 13983\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph