Elliptic curve isogeny class 484.2-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-484.2-c
• Conductor: 484.2
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 484.2-c over \(\Q(\sqrt{3}) \)

Isogeny class 484.2-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
484.2-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 43 a + 75\bigr] \)
484.2-c2	\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -43 a - 75\bigr] \)
484.2-c3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 110 a - 206\) , \( -916 a + 1570\bigr] \)
484.2-c4	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 110 a - 206\) , \( 916 a - 1570\bigr] \)
484.2-c5	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 5 a - 16\) , \( -14 a + 30\bigr] \)
484.2-c6	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 5 a - 16\) , \( 14 a - 30\bigr] \)
484.2-c7	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -20 a - 86\) , \( 154 a + 210\bigr] \)
484.2-c8	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -20 a - 86\) , \( -154 a - 210\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 2 & 6 & 4 & 12 \\ 3 & 1 & 12 & 4 & 6 & 2 & 12 & 4 \\ 4 & 12 & 1 & 12 & 2 & 6 & 4 & 3 \\ 12 & 4 & 12 & 1 & 6 & 2 & 3 & 4 \\ 2 & 6 & 2 & 6 & 1 & 3 & 2 & 6 \\ 6 & 2 & 6 & 2 & 3 & 1 & 6 & 2 \\ 4 & 12 & 4 & 3 & 2 & 6 & 1 & 12 \\ 12 & 4 & 3 & 4 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph