Elliptic curve isogeny class 27.3-a over number field \(\Q(\sqrt{-23}) \)

• Base field: \(\Q(\sqrt{-23}) \)
• Label: 2.0.23.1-27.3-a
• Conductor: 27.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 27.3-a over \(\Q(\sqrt{-23}) \)

Isogeny class 27.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
27.3-a1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10 a + 47\) , \( -32 a + 94\bigr] \)
27.3-a2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 4 a + 11\) , \( 14 a - 20\bigr] \)
27.3-a3	\( \bigl[a\) , \( -1\) , \( a\) , \( 14 a - 1\) , \( -35 a - 53\bigr] \)
27.3-a4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 14 a - 36\bigr] \)
27.3-a5	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2 a + 1\) , \( 0\bigr] \)
27.3-a6	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -8 a - 4\) , \( -22 a + 43\bigr] \)
27.3-a7	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 17 a - 98\) , \( 53 a - 309\bigr] \)
27.3-a8	\( \bigl[a\) , \( -1\) , \( a\) , \( 239 a - 91\) , \( -1655 a - 3293\bigr] \)

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