Elliptic curve isogeny class 108.6-b over number field \(\Q(\sqrt{-23}) \)

• Base field: \(\Q(\sqrt{-23}) \)
• Label: 2.0.23.1-108.6-b
• Conductor: 108.6
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 6 \); class number \(3\).

Elliptic curves in class 108.6-b over \(\Q(\sqrt{-23}) \)

Isogeny class 108.6-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
108.6-b1	\( \bigl[a\) , \( a\) , \( 0\) , \( -23 a + 894\) , \( -3847 a + 802\bigr] \)
108.6-b2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -63 a + 190\) , \( 193 a + 871\bigr] \)
108.6-b3	\( \bigl[a\) , \( a\) , \( 0\) , \( -3 a + 54\) , \( -43 a + 10\bigr] \)
108.6-b4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 23\) , \( 37 a + 83\bigr] \)
108.6-b5	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 34\) , \( -39 a - 73\bigr] \)
108.6-b6	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -3 a + 10\) , \( a + 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 8 & 4 & 4 \\ 8 & 1 & 4 & 4 & 8 & 2 \\ 2 & 4 & 1 & 4 & 2 & 2 \\ 8 & 4 & 4 & 1 & 8 & 2 \\ 4 & 8 & 2 & 8 & 1 & 4 \\ 4 & 2 & 2 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph