Elliptic curve isogeny class 27.2-a over number field \(\Q(\sqrt{-23}) \)

• Base field: \(\Q(\sqrt{-23}) \)
• Label: 2.0.23.1-27.2-a
• Conductor: 27.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 27.2-a over \(\Q(\sqrt{-23}) \)

Isogeny class 27.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
27.2-a1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -2 a + 13\) , \( -11 a - 20\bigr] \)
27.2-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( -10 a + 60\) , \( 93 a + 58\bigr] \)
27.2-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -16 a + 13\) , \( 34 a - 88\bigr] \)
27.2-a4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 1\) , \( a - 2\bigr] \)
27.2-a5	\( \bigl[a\) , \( a\) , \( 0\) , \( -2 a + 12\) , \( -a - 26\bigr] \)
27.2-a6	\( \bigl[a\) , \( a\) , \( 0\) , \( -17 a - 78\) , \( -130 a - 80\bigr] \)
27.2-a7	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 10 a - 14\) , \( 13 a + 34\bigr] \)
27.2-a8	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -241 a + 148\) , \( 1654 a - 4948\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 4 & 8 & 2 & 4 & 16 & 8 \\ 16 & 1 & 4 & 2 & 8 & 16 & 4 & 8 \\ 4 & 4 & 1 & 2 & 2 & 4 & 4 & 2 \\ 8 & 2 & 2 & 1 & 4 & 8 & 2 & 4 \\ 2 & 8 & 2 & 4 & 1 & 2 & 8 & 4 \\ 4 & 16 & 4 & 8 & 2 & 1 & 16 & 8 \\ 16 & 4 & 4 & 2 & 8 & 16 & 1 & 8 \\ 8 & 8 & 2 & 4 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph