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

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

Isogeny class 14400.4-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14400.4-e1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 29 a + 39\) , \( -103 a + 252\bigr] \)
14400.4-e2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 79\) , \( 45 a + 720\bigr] \)
14400.4-e3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -151 a - 841\) , \( 3437 a + 8392\bigr] \)
14400.4-e4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -871 a + 1639\) , \( 4845 a + 26520\bigr] \)

Rank

Rank: \( 0 \)

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