Elliptic curve isogeny class 16.5-b over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-16.5-b
• Conductor: 16.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 16.5-b over \(\Q(\sqrt{89}) \)

Isogeny class 16.5-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
16.5-b1	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 29330 a - 153014\) , \( 5955680 a - 31070736\bigr] \)
16.5-b2	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -20 a - 84\) , \( 390 a + 1642\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph