Elliptic curve isogeny class 14.1-b over number field \(\Q(\sqrt{161}) \)

• Base field: \(\Q(\sqrt{161}) \)
• Label: 2.2.161.1-14.1-b
• Conductor: 14.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 14.1-b over \(\Q(\sqrt{161}) \)

Isogeny class 14.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
14.1-b1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -817 a - 4693\) , \( 30200 a + 176632\bigr] \)
14.1-b2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 18 a + 187\) , \( 267 a + 1695\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph