Elliptic curve isogeny class 1089.2-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-1089.2-c
• Conductor: 1089.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1089.2-c over \(\Q(\sqrt{-11}) \)

Isogeny class 1089.2-c contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
1089.2-c1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -4 a + 57\) , \( 115 a - 29\bigr] \)
1089.2-c2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 3 a + 54\) , \( -115 a + 86\bigr] \)
1089.2-c3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -4 a + 2\) , \( 5 a - 7\bigr] \)
1089.2-c4	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 3 a - 1\) , \( -5 a - 2\bigr] \)
1089.2-c5	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -52 a + 109\) , \( -49 a + 614\bigr] \)
1089.2-c6	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 51 a + 57\) , \( 49 a + 565\bigr] \)
1089.2-c7	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 58 a + 879\) , \( -6561 a + 4970\bigr] \)
1089.2-c8	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -59 a + 937\) , \( 6561 a - 1591\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 2 & 10 & 10 & 2 & 10 & 2 \\ 5 & 1 & 10 & 2 & 2 & 10 & 2 & 10 \\ 2 & 10 & 1 & 5 & 20 & 4 & 20 & 4 \\ 10 & 2 & 5 & 1 & 4 & 20 & 4 & 20 \\ 10 & 2 & 20 & 4 & 1 & 20 & 4 & 5 \\ 2 & 10 & 4 & 20 & 20 & 1 & 5 & 4 \\ 10 & 2 & 20 & 4 & 4 & 5 & 1 & 20 \\ 2 & 10 & 4 & 20 & 5 & 4 & 20 & 1 \end{array}\right)\)

Isogeny graph