Elliptic curve isogeny class 45369.4-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-45369.4-a
• Conductor: 45369.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 45369.4-a over \(\Q(\sqrt{-11}) \)

Isogeny class 45369.4-a contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
45369.4-a1	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -56 a + 380\) , \( 1638 a + 320\bigr] \)
45369.4-a2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -98 a + 376\) , \( -1317 a - 1012\bigr] \)
45369.4-a3	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 19 a + 10\) , \( 42 a + 128\bigr] \)
45369.4-a4	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 197 a + 601\) , \( 2835 a - 10405\bigr] \)
45369.4-a5	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -23 a + 6\) , \( -108 a + 81\bigr] \)
45369.4-a6	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -426 a + 525\) , \( 3560 a - 9834\bigr] \)
45369.4-a7	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1593 a + 6071\) , \( -81345 a - 68971\bigr] \)
45369.4-a8	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -886 a + 6155\) , \( 98920 a + 17102\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph