Elliptic curve isogeny class 14400.4-f over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.4-f
• Conductor: 14400.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 14400.4-f over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.4-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
14400.4-f1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 48 a - 32\) , \( -720 a + 1980\bigr] \)
14400.4-f2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a - 2\) , \( 0\bigr] \)
14400.4-f3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a + 8\) , \( 16 a - 44\bigr] \)
14400.4-f4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -72 a + 48\) , \( -144 a + 396\bigr] \)
14400.4-f5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -192 a + 128\) , \( 880 a - 2420\bigr] \)
14400.4-f6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1152 a + 768\) , \( -11088 a + 30492\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph