Elliptic curve isogeny class 36100.2-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-36100.2-f
• Conductor: 36100.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 36100.2-f over \(\Q(\sqrt{-3}) \)

Isogeny class 36100.2-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36100.2-f1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 227 a - 44\) , \( -450 a - 927\bigr] \)
36100.2-f2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 27 a + 36\) , \( -130 a + 161\bigr] \)
36100.2-f3	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 1067 a - 1773\) , \( 16017 a - 11100\bigr] \)
36100.2-f4	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 337 a - 873\) , \( -5073 a + 8888\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph