Elliptic curve isogeny class 10.4-a over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-10.4-a
• Conductor: 10.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.4-a over \(\Q(\sqrt{89}) \)

Isogeny class 10.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
10.4-a1	\( \bigl[1\) , \( -a\) , \( 1\) , \( a + 10\) , \( -2 a - 6\bigr] \)
10.4-a2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 267 a - 1379\) , \( 4862 a - 25355\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph