Elliptic curve isogeny class 36864.1-q over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-36864.1-q
• Conductor: 36864.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 36864.1-q over \(\Q(\sqrt{-3}) \)

Isogeny class 36864.1-q contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36864.1-q1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 253 a - 128\) , \( 902 a + 477\bigr] \)
36864.1-q2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 13 a - 128\) , \( -58 a + 621\bigr] \)
36864.1-q3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 7\) , \( 5 a - 3\bigr] \)
36864.1-q4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 13 a - 8\) , \( 14 a + 21\bigr] \)