Elliptic curve isogeny class 26.4-a over number field \(\Q(\sqrt{-23}) \)

• Base field: \(\Q(\sqrt{-23}) \)
• Label: 2.0.23.1-26.4-a
• Conductor: 26.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 26.4-a over \(\Q(\sqrt{-23}) \)

Isogeny class 26.4-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
26.4-a1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -10 a - 11\) , \( -26 a - 32\bigr] \)
26.4-a2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
26.4-a3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( -a - 29\bigr] \)
26.4-a4	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -825 a - 1201\) , \( -19455 a - 2805\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 9 & 3 & 3 \\ 9 & 1 & 3 & 27 \\ 3 & 3 & 1 & 9 \\ 3 & 27 & 9 & 1 \end{array}\right)\)

Isogeny graph