Elliptic curve isogeny class 43776.1-o over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.1-o
• Conductor: 43776.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 43776.1-o over \(\Q(\sqrt{-3}) \)

Isogeny class 43776.1-o contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
43776.1-o1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -75 a + 147\) , \( -552 a - 118\bigr] \)
43776.1-o2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 405 a - 93\) , \( -888 a - 3478\bigr] \)
43776.1-o3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 13\) , \( 8 a - 6\bigr] \)
43776.1-o4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 85 a - 173\) , \( 568 a - 790\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph