Elliptic curve isogeny class 10.1-a over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-10.1-a
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-a over \(\Q(\sqrt{89}) \)

Isogeny class 10.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
10.1-a1	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a + 11\) , \( 2 a - 8\bigr] \)
10.1-a2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -265 a - 1114\) , \( -4596 a - 19380\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph