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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.2-f
• Conductor: 43776.2
• Rank: \( 0 \)

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

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

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

Isogeny class 43776.2-f contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
43776.2-f1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6761 a - 1711\) , \( -232201 a - 80360\bigr] \)
43776.2-f2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 41 a - 31\) , \( -25 a + 280\bigr] \)
43776.2-f3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -919 a - 1711\) , \( -15625 a - 32744\bigr] \)
43776.2-f4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -439 a + 449\) , \( 359 a + 2872\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph