Elliptic Curve Isogeny Class 18.1-a over Number Field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-18.1-a
• Conductor: 18.1
• Rank: not recorded

Base field \(\Q(\sqrt{89}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 22 \); class number \(1\).

Elliptic curves in class 18.1-a over \(\Q(\sqrt{89}) \)

Isogeny class 18.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
18.1-a1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 254 a - 1320\) , \( 1589 a - 8304\bigr] \)
18.1-a2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -42 a - 171\) , \( -194 a - 821\bigr] \)
18.1-a3	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -85208 a - 359311\) , \( 26726360 a + 112704799\bigr] \)
18.1-a4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -1330193 a - 5609401\) , \( 1811710118 a + 7639964467\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph