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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.6-e
• Conductor: 14400.6
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 14400.6-e over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.6-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14400.6-e1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 88 a - 288\) , \( -192 a - 2052\bigr] \)
14400.6-e2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -52 a + 92\) , \( 8 a - 452\bigr] \)
14400.6-e3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a + 37\) , \( 30 a + 24\bigr] \)
14400.6-e4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -832 a + 1352\) , \( -1600 a - 26516\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph