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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.2-d
• Conductor: 43776.2
• Rank: \( 1 \)

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

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

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

Isogeny class 43776.2-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
43776.2-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 264 a - 519\) , \( 3036 a - 4074\bigr] \)
43776.2-d2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -103 a - 31\) , \( -951 a + 312\bigr] \)
43776.2-d3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -23 a + 49\) , \( -87 a - 24\bigr] \)
43776.2-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 39\) , \( 12 a - 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph