Elliptic Curve Isogeny Class 108.1-a over Number Field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-108.1-a
• Conductor: 108.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 108.1-a over \(\Q(\sqrt{-11}) \)

Isogeny class 108.1-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
108.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 443 a - 974\) , \( 6754 a - 9107\bigr] \)
108.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3 a - 14\) , \( 2 a - 11\bigr] \)
108.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 1\) , \( a - 1\bigr] \)
108.1-a4	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 1\) , \( 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 27 \\ 3 & 1 & 3 & 9 \\ 9 & 3 & 1 & 3 \\ 27 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph