Elliptic curve isogeny class 14.2-a over number field \(\Q(\sqrt{161}) \)

• Base field: \(\Q(\sqrt{161}) \)
• Label: 2.2.161.1-14.2-a
• Conductor: 14.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 14.2-a over \(\Q(\sqrt{161}) \)

Isogeny class 14.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
14.2-a1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -20094 a - 117387\) , \( 1576182 a + 9211722\bigr] \)
14.2-a2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -845179 a - 4939422\) , \( -1067667727 a - 6239758448\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph