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

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

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

Curve label	Weierstrass Coefficients
14400.6-j1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a + 32\) , \( 2 a + 32\bigr] \)
14400.6-j2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a - 133\) , \( -131 a + 143\bigr] \)
14400.6-j3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -7 a + 327\) , \( 1447 a - 408\bigr] \)
14400.6-j4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 48 a + 392\) , \( -1780 a + 1976\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph