Elliptic curve isogeny class 14400.5-f over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.5-f
• Conductor: 14400.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 14400.5-f over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.5-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
14400.5-f1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -65 a - 55\) , \( 395 a - 23\bigr] \)
14400.5-f2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 5\) , \( 11 a + 13\bigr] \)
14400.5-f3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 215 a - 135\) , \( -1229 a - 687\bigr] \)
14400.5-f4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 55 a - 15\) , \( 75 a + 225\bigr] \)
14400.5-f5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 10\) , \( 4 a + 9\bigr] \)
14400.5-f6	\( \bigl[0\) , \( -1\) , \( 0\) , \( 855 a - 215\) , \( 6435 a + 14385\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph