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

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

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

Curve label	Weierstrass Coefficients
112896.2-h1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 36 a - 27\) , \( -90 a + 36\bigr] \)
112896.2-h2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 336 a + 168\) , \( -2280 a + 4236\bigr] \)
112896.2-h3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 36 a - 12\) , \( -144 a + 108\bigr] \)
112896.2-h4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 96 a + 528\) , \( 3528 a + 3420\bigr] \)
112896.2-h5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -264 a + 48\) , \( -1224 a + 828\bigr] \)
112896.2-h6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5376 a + 2688\) , \( -132312 a + 267324\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph