Elliptic curve isogeny class 27225.8-f over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-27225.8-f
• Conductor: 27225.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 27225.8-f over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.8-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
27225.8-f1	\( \bigl[a\) , \( -1\) , \( 1\) , \( -1739 a - 885\) , \( -2648 a + 24541\bigr] \)
27225.8-f2	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3646 a - 21896\) , \( 302918 a - 1131650\bigr] \)
27225.8-f3	\( \bigl[a\) , \( -1\) , \( 1\) , \( -21649 a - 4570\) , \( -1749954 a + 1418945\bigr] \)
27225.8-f4	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3756 a - 21511\) , \( 295262 a - 1181546\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph