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

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

Isogeny class 14400.5-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
14400.5-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 35 a - 95\) , \( 735 a - 2643\bigr] \)
14400.5-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 65 a - 360\) , \( 25 a + 600\bigr] \)
14400.5-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3665 a + 3705\) , \( -10725 a + 147897\bigr] \)
14400.5-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1295 a + 985\) , \( 5019 a - 55671\bigr] \)
14400.5-c5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1465 a + 905\) , \( 18035 a - 43343\bigr] \)
14400.5-c6	\( \bigl[0\) , \( -1\) , \( 0\) , \( 50 a - 225\) , \( 394 a - 1146\bigr] \)
14400.5-c7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -23265 a + 14105\) , \( 1129995 a - 2823383\bigr] \)
14400.5-c8	\( \bigl[0\) , \( -1\) , \( 0\) , \( 800 a - 3600\) , \( 26044 a - 77196\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 4 & 2 & 2 & 2 & 4 & 4 \\ 4 & 1 & 16 & 8 & 8 & 2 & 16 & 4 \\ 4 & 16 & 1 & 8 & 2 & 8 & 4 & 16 \\ 2 & 8 & 8 & 1 & 4 & 4 & 8 & 8 \\ 2 & 8 & 2 & 4 & 1 & 4 & 2 & 8 \\ 2 & 2 & 8 & 4 & 4 & 1 & 8 & 2 \\ 4 & 16 & 4 & 8 & 2 & 8 & 1 & 16 \\ 4 & 4 & 16 & 8 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph