Elliptic curve isogeny class 675.5-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-675.5-b
• Conductor: 675.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 675.5-b over \(\Q(\sqrt{-11}) \)

Isogeny class 675.5-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
675.5-b1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 7 a - 3\) , \( -11 a - 9\bigr] \)
675.5-b2	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -3 a - 12\) , \( 2 a + 19\bigr] \)
675.5-b3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 2 a + 12\) , \( -34 a + 6\bigr] \)
675.5-b4	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -8 a + 3\) , \( -a + 64\bigr] \)
675.5-b5	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 77 a + 63\) , \( -104 a + 706\bigr] \)
675.5-b6	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -88 a - 33\) , \( -448 a + 339\bigr] \)
675.5-b7	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -173 a + 183\) , \( -310 a + 2242\bigr] \)
675.5-b8	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 12 a + 297\) , \( -1192 a + 753\bigr] \)

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