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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-112896.2-k
• 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-k over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
112896.2-k1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 193\) , \( -2567 a + 1380\bigr] \)
112896.2-k2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 18527\) , \( -434855 a + 208164\bigr] \)
112896.2-k3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4993\) , \( -53831 a + 29412\bigr] \)
112896.2-k4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 43873\) , \( 4059673 a - 2007900\bigr] \)
112896.2-k5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4033\) , \( -112391 a + 58212\bigr] \)
112896.2-k6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 64513\) , \( -7261127 a + 3662820\bigr] \)

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