Elliptic curve isogeny class 12288.1-h over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12288.1-h
• Conductor: 12288.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 12288.1-h over \(\Q(\sqrt{-3}) \)

Isogeny class 12288.1-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
12288.1-h1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -31 a\) , \( -33\bigr] \)
12288.1-h2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a\) , \( -9\bigr] \)
12288.1-h3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a\) , \( 2\bigr] \)
12288.1-h4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 129 a\) , \( -609\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph