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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.2-i
• 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-i over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
43776.2-i1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -88 a + 173\) , \( -568 a - 222\bigr] \)
43776.2-i2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 312 a + 93\) , \( 888 a - 4366\bigr] \)
43776.2-i3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 72 a - 147\) , \( 552 a - 670\bigr] \)
43776.2-i4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 13\) , \( -8 a + 2\bigr] \)

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