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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-768.1-h
• 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-h over \(\Q(\sqrt{3}) \)

Isogeny class 768.1-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
768.1-h1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 4\) , \( 4 a - 8\bigr] \)
768.1-h2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a - 4\) , \( 2 a + 4\bigr] \)
768.1-h3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -12 a - 34\) , \( -46 a - 56\bigr] \)
768.1-h4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -32 a - 54\) , \( 138 a + 240\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph