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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.4-b
• Conductor: 14400.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 14400.4-b over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.4-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
14400.4-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 312 a + 984\) , \( -8388 a + 14004\bigr] \)
14400.4-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 707 a - 71\) , \( -4329 a - 12627\bigr] \)
14400.4-b3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 727 a - 751\) , \( 4475 a - 28463\bigr] \)
14400.4-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 42 a + 39\) , \( -234 a + 18\bigr] \)
14400.4-b5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -263 a - 216\) , \( -2055 a + 432\bigr] \)
14400.4-b6	\( \bigl[0\) , \( -1\) , \( 0\) , \( 11327 a - 1151\) , \( -264573 a - 807831\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph