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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.6-l
• Conductor: 14400.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 14400.6-l over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.6-l contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
14400.6-l1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -46 a + 15\) , \( 673 a + 1275\bigr] \)
14400.6-l2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a\) , \( -2 a\bigr] \)
14400.6-l3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 5\) , \( -3 a - 33\bigr] \)
14400.6-l4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a - 25\) , \( 217 a + 227\bigr] \)
14400.6-l5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 194 a - 65\) , \( -687 a - 1605\bigr] \)
14400.6-l6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1154 a - 385\) , \( 12241 a + 19019\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph