Elliptic curve isogeny class 2.2-a over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-2.2-a
• Conductor: 2.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 2.2-a over \(\Q(\sqrt{89}) \)

Isogeny class 2.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
2.2-a1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -1517 a - 6400\) , \( 99636 a + 420163\bigr] \)
2.2-a2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 4 a + 11\) , \( 6 a + 23\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph