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

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

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

Curve label	Weierstrass Coefficients
14400.4-r1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -113 a - 191\) , \( -1087 a - 729\bigr] \)
14400.4-r2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 552 a - 176\) , \( -3600 a - 6912\bigr] \)
14400.4-r3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 152 a + 424\) , \( -2352 a + 4656\bigr] \)
14400.4-r4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 32 a + 4\) , \( -96 a - 48\bigr] \)
14400.4-r5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -63 a - 16\) , \( 255 a - 232\bigr] \)
14400.4-r6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -8 a - 11\) , \( -16 a - 18\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph