Elliptic curve isogeny class 108.3-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-108.3-a
• Conductor: 108.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 108.3-a over \(\Q(\sqrt{-11}) \)

Isogeny class 108.3-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
108.3-a1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -3 a + 14\) , \( 10 a + 2\bigr] \)
108.3-a2	\( \bigl[1\) , \( -a\) , \( a\) , \( 8 a - 4\) , \( 7 a + 20\bigr] \)
108.3-a3	\( \bigl[1\) , \( -a\) , \( a\) , \( -2 a - 24\) , \( 15 a + 90\bigr] \)
108.3-a4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -13 a - 6\) , \( 62 a - 38\bigr] \)
108.3-a5	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -3 a - 8\) , \( -2 a + 5\bigr] \)
108.3-a6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -43 a - 88\) , \( 206 a + 277\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 18 & 2 & 3 & 6 \\ 9 & 1 & 2 & 18 & 3 & 6 \\ 18 & 2 & 1 & 9 & 6 & 3 \\ 2 & 18 & 9 & 1 & 6 & 3 \\ 3 & 3 & 6 & 6 & 1 & 2 \\ 6 & 6 & 3 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph