Elliptic curve isogeny class 112896.2-u over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-112896.2-u
• Conductor: 112896.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 112896.2-u over \(\Q(\sqrt{-3}) \)

Isogeny class 112896.2-u contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
112896.2-u1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -192 a\) , \( 2760 a - 1380\bigr] \)
112896.2-u2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18528 a\) , \( 416328 a - 208164\bigr] \)
112896.2-u3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4992 a\) , \( 58824 a - 29412\bigr] \)
112896.2-u4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -43872 a\) , \( -4015800 a + 2007900\bigr] \)
112896.2-u5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4032 a\) , \( 116424 a - 58212\bigr] \)
112896.2-u6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -64512 a\) , \( 7325640 a - 3662820\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph