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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.1-b
• 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-b over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
43776.1-b1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -48 a + 24\) , \( 112 a - 160\bigr] \)
43776.1-b2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a + 104\) , \( 816 a - 608\bigr] \)
43776.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 39 a - 24\) , \( -12 a - 30\bigr] \)
43776.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 519 a - 264\) , \( -3036 a - 1038\bigr] \)

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