Elliptic curve isogeny class 2.1-a over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-2.1-a
• Conductor: 2.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2.1-a over \(\Q(\sqrt{89}) \)

Isogeny class 2.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
2.1-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 1515 a - 7916\) , \( -99637 a + 519800\bigr] \)
2.1-a2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 8 a + 27\) , \( 16 a + 63\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph