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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-768.1-c
• Conductor: 768.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
768.1-c1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 41\) , \( 11 a + 177\bigr] \)
768.1-c2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 200974 a - 348097\) , \( 64360541 a - 111475727\bigr] \)
768.1-c3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12804 a - 22177\) , \( 955655 a - 1655243\bigr] \)
768.1-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -43196 a + 74818\) , \( 28011318 a - 48517026\bigr] \)
768.1-c5	\( \bigl[0\) , \( -1\) , \( 0\) , \( 216 a - 374\) , \( -1926 a + 3336\bigr] \)
768.1-c6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -444 a + 766\) , \( -10806 a + 18720\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph