Elliptic curve isogeny class 72.7-a over number field \(\Q(\sqrt{-23}) \)

• Base field: \(\Q(\sqrt{-23}) \)
• Label: 2.0.23.1-72.7-a
• Conductor: 72.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 72.7-a over \(\Q(\sqrt{-23}) \)

Isogeny class 72.7-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
72.7-a1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 18 a + 85\) , \( -117 a + 249\bigr] \)
72.7-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 5\) , \( -6 a - 1\bigr] \)
72.7-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( -a - 21\) , \( -12 a - 36\bigr] \)
72.7-a4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -5 a - 17\) , \( -5 a + 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph