Elliptic curve isogeny class 108.4-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-108.4-a
• Conductor: 108.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 108.4-a over \(\Q(\sqrt{-11}) \)

Isogeny class 108.4-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
108.4-a1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -445 a - 529\) , \( -7728 a - 1018\bigr] \)
108.4-a2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -5 a - 9\) , \( -16 a + 6\bigr] \)
108.4-a3	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)
108.4-a4	\( \bigl[1\) , \( -a\) , \( a\) , \( a\) , \( -a + 4\bigr] \)

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