Elliptic curve isogeny class 36100.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-36100.3-a
• Conductor: 36100.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 36100.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 36100.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36100.3-a1	\( \bigl[a\) , \( a\) , \( a\) , \( -54 a + 41\) , \( 57 a - 150\bigr] \)
36100.3-a2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -32 a - 10\) , \( 9 a - 41\bigr] \)
36100.3-a3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 128 a + 40\) , \( 71 a - 157\bigr] \)
36100.3-a4	\( \bigl[a\) , \( a\) , \( a\) , \( -894 a + 681\) , \( 3441 a - 9742\bigr] \)

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