Elliptic curve isogeny class 72.1-a over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-72.1-a
• Conductor: 72.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 23 \); class number \(1\).

Elliptic curves in class 72.1-a over \(\Q(\sqrt{23}) \)

Isogeny class 72.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
72.1-a1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -942 a + 4522\) , \( 248884 a - 1193604\bigr] \)
72.1-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-a3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 258 a - 1233\) , \( -3006 a + 14418\bigr] \)
72.1-a4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1458 a - 6988\) , \( 67524 a - 323832\bigr] \)
72.1-a5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 3858 a - 18498\) , \( -275046 a + 1319076\bigr] \)
72.1-a6	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -23058 a - 110578\) , \( -4238844 a - 20328780\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph