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

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

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

Curve label	Weierstrass Coefficients
112896.2-g1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 28 a - 35\) , \( 82 a - 81\bigr] \)
112896.2-g2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -167 a - 335\) , \( 1777 a + 2124\bigr] \)
112896.2-g3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 13 a - 35\) , \( 121 a - 48\bigr] \)
112896.2-g4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -527 a - 95\) , \( -4151 a + 7476\bigr] \)
112896.2-g5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -47 a + 265\) , \( 1441 a - 348\bigr] \)
112896.2-g6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2687 a - 5375\) , \( 124249 a + 137700\bigr] \)

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