Elliptic curve isogeny class 16.2-b over number field \(\Q(\sqrt{161}) \)

• Base field: \(\Q(\sqrt{161}) \)
• Label: 2.2.161.1-16.2-b
• Conductor: 16.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{161}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 40 \); class number \(1\).

Elliptic curves in class 16.2-b over \(\Q(\sqrt{161}) \)

Isogeny class 16.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.2-b1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -124579001 a - 728075652\) , \( 1960119291129 a + 11455503161448\bigr] \)
16.2-b2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -2009050021 a - 11741468472\) , \( 123450894141641 a + 721482674306200\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph