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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.5-g
• Conductor: 14400.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 14400.5-g over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.5-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14400.5-g1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 7\) , \( 2 a + 10\bigr] \)
14400.5-g2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 12\) , \( 24 a + 36\bigr] \)
14400.5-g3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a + 88\) , \( 224 a - 324\bigr] \)
14400.5-g4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 256 a - 192\) , \( 1632 a + 1260\bigr] \)

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