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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.6-r
• 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-r over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
14400.6-r1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 113 a - 304\) , \( 1087 a - 1816\bigr] \)
14400.6-r2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -552 a + 376\) , \( 3600 a - 10512\bigr] \)
14400.6-r3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -152 a + 576\) , \( 2352 a + 2304\bigr] \)
14400.6-r4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -32 a + 36\) , \( 96 a - 144\bigr] \)
14400.6-r5	\( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 19\) , \( 16 a - 34\bigr] \)
14400.6-r6	\( \bigl[0\) , \( 1\) , \( 0\) , \( 63 a - 79\) , \( -255 a + 23\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph