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

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

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

Curve label	Weierstrass Coefficients
43776.1-g1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a + 6\) , \( 12 a - 6\bigr] \)
43776.1-g2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 18 a - 9\) , \( 45 a - 9\bigr] \)
43776.1-g3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -42 a - 69\) , \( 153 a + 243\bigr] \)
43776.1-g4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 318 a - 189\) , \( 1809 a + 27\bigr] \)

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