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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.4-g
• 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-g over \(\Q(\sqrt{-11}) \)

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

Curve label	Weierstrass Coefficients
14400.4-g1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -342 a + 503\) , \( -233 a - 7703\bigr] \)
14400.4-g2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 23 a - 32\) , \( 66 a + 6\bigr] \)
14400.4-g3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -7 a - 137\) , \( 177 a + 732\bigr] \)
14400.4-g4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 38 a + 83\) , \( 251 a - 659\bigr] \)
14400.4-g5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 658 a + 1503\) , \( 14895 a - 35055\bigr] \)
14400.4-g6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 368 a - 512\) , \( 4140 a - 1260\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph