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

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

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

Curve label	Weierstrass Coefficients
43776.2-c1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -5 a - 2\) , \( -4 a\bigr] \)
43776.2-c2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 70 a + 43\) , \( -265 a + 465\bigr] \)
43776.2-c3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 17\) , \( -37 a + 45\bigr] \)
43776.2-c4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 190 a - 317\) , \( -1681 a + 2025\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph