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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.5-r
• 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-r over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
14400.5-r1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 641 a + 319\) , \( 819 a - 17460\bigr] \)
14400.5-r2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -24 a + 104\) , \( -172 a - 76\bigr] \)
14400.5-r3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 41 a + 19\) , \( 39 a - 300\bigr] \)
14400.5-r4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( -2 a - 6\bigr] \)
14400.5-r5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 81 a - 41\) , \( 363 a - 276\bigr] \)
14400.5-r6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a - 41\) , \( -83 a - 69\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph