Elliptic curve isogeny class 225.8-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-225.8-a
• Conductor: 225.8
• Rank: \( 1 \)

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

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

Elliptic curves in class 225.8-a over \(\Q(\sqrt{-11}) \)

Isogeny class 225.8-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
225.8-a1	\( \bigl[1\) , \( -a\) , \( 1\) , \( -6 a - 11\) , \( 18 a\bigr] \)
225.8-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -6 a - 11\) , \( 12 a + 15\bigr] \)
225.8-a3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \)
225.8-a4	\( \bigl[1\) , \( -a\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph