Elliptic curve isogeny class 14400.6-i over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.6-i
• Conductor: 14400.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 14400.6-i over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.6-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
14400.6-i1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12046 a - 10585\) , \( -929137 a + 55513\bigr] \)
14400.6-i2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12766 a - 7345\) , \( -943681 a - 343439\bigr] \)
14400.6-i3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -706 a - 865\) , \( -13837 a + 6913\bigr] \)
14400.6-i4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 54 a + 340\) , \( -1821 a + 66\bigr] \)
14400.6-i5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1526 a - 10425\) , \( 88839 a + 413721\bigr] \)
14400.6-i6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -192766 a - 169345\) , \( -60012193 a + 3953665\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 2 & 4 & 4 & 2 \\ 2 & 1 & 4 & 8 & 8 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 8 & 2 & 4 & 1 & 8 \\ 2 & 4 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph