Elliptic curve isogeny class 196.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-196.2-a
• Conductor: 196.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 196.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 196.2-a contains 10 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
196.2-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
196.2-a2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a\) , \( 0\bigr] \)
196.2-a3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a - 5\) , \( -6\bigr] \)
196.2-a4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -36 a + 35\) , \( -70\bigr] \)
196.2-a5	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 184 a - 415\) , \( 1880 a - 2686\bigr] \)
196.2-a6	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 414 a - 185\) , \( -1880 a - 806\bigr] \)
196.2-a7	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -11 a + 10\) , \( 12\bigr] \)
196.2-a8	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 184 a - 405\) , \( 1920 a - 2854\bigr] \)
196.2-a9	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 404 a - 185\) , \( -1920 a - 934\bigr] \)
196.2-a10	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 9 & 3 & 6 & 18 & 18 & 18 & 9 & 9 & 2 \\ 9 & 1 & 3 & 6 & 18 & 18 & 2 & 9 & 9 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 & 6 & 3 & 3 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 & 3 & 6 & 6 & 3 \\ 18 & 18 & 6 & 3 & 1 & 9 & 9 & 2 & 18 & 9 \\ 18 & 18 & 6 & 3 & 9 & 1 & 9 & 18 & 2 & 9 \\ 18 & 2 & 6 & 3 & 9 & 9 & 1 & 18 & 18 & 9 \\ 9 & 9 & 3 & 6 & 2 & 18 & 18 & 1 & 9 & 18 \\ 9 & 9 & 3 & 6 & 18 & 2 & 18 & 9 & 1 & 18 \\ 2 & 18 & 6 & 3 & 9 & 9 & 9 & 18 & 18 & 1 \end{array}\right)\)

Isogeny graph