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

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

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

Curve label	Weierstrass Coefficients
14400.4-n1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12048 a - 22632\) , \( 941184 a - 896256\bigr] \)
14400.4-n2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1528 a - 11952\) , \( -87312 a + 490608\bigr] \)
14400.4-n3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12768 a - 20112\) , \( 956448 a - 1307232\bigr] \)
14400.4-n4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -52 a + 393\) , \( 1768 a - 1362\bigr] \)
14400.4-n5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 708 a - 1572\) , \( 14544 a - 8496\bigr] \)
14400.4-n6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 192768 a - 362112\) , \( 60204960 a - 56420640\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph