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

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

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

Curve label	Weierstrass Coefficients
14400.5-e1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a + 5\) , \( -4 a + 13\bigr] \)
14400.5-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 65 a - 120\) , \( -395 a + 372\bigr] \)
14400.5-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a\) , \( -11 a + 24\bigr] \)
14400.5-e4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -55 a + 40\) , \( -75 a + 300\bigr] \)
14400.5-e5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -215 a + 80\) , \( 1229 a - 1916\bigr] \)
14400.5-e6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -855 a + 640\) , \( -6435 a + 20820\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph