Elliptic curve isogeny class 675.8-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-675.8-b
• Conductor: 675.8
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-11}) \)

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

Elliptic curves in class 675.8-b over \(\Q(\sqrt{-11}) \)

Isogeny class 675.8-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
675.8-b1	\( \bigl[1\) , \( -a\) , \( 0\) , \( 3 a - 15\) , \( -2 a + 21\bigr] \)
675.8-b2	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -9 a + 5\) , \( 10 a - 19\bigr] \)
675.8-b3	\( \bigl[1\) , \( -a\) , \( 0\) , \( 8 a - 5\) , \( a + 63\bigr] \)
675.8-b4	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -4 a + 15\) , \( 33 a - 27\bigr] \)
675.8-b5	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 86 a - 120\) , \( 447 a - 108\bigr] \)
675.8-b6	\( \bigl[1\) , \( -a\) , \( 0\) , \( -77 a + 140\) , \( 104 a + 602\bigr] \)
675.8-b7	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -14 a + 310\) , \( 1191 a - 438\bigr] \)
675.8-b8	\( \bigl[1\) , \( -a\) , \( 0\) , \( 173 a + 10\) , \( 310 a + 1932\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph