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

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

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

Curve label	Weierstrass Coefficients
14400.6-m1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -21 a - 10\) , \( -88 a + 62\bigr] \)
14400.6-m2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 344 a + 160\) , \( 576 a - 7776\bigr] \)
14400.6-m3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 9 a - 145\) , \( -169 a + 764\bigr] \)
14400.6-m4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -36 a + 120\) , \( -288 a - 288\bigr] \)
14400.6-m5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -656 a + 2160\) , \( -15552 a - 18000\bigr] \)
14400.6-m6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -366 a - 145\) , \( -4507 a + 2735\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph