Elliptic curve isogeny class 43776.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.2-a
• Conductor: 43776.2
• Rank: \( 2 \)

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

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

Elliptic curves in class 43776.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 43776.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
43776.2-a1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -126 a + 1023\) , \( 13401 a - 4221\bigr] \)
43776.2-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 63\) , \( 225 a - 45\bigr] \)
43776.2-a3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 114 a + 63\) , \( -87 a + 867\bigr] \)
43776.2-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 3\) , \( 9 a - 9\bigr] \)

Rank

Rank: \( 2 \)

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