Elliptic curve isogeny class 10.3-f over number field \(\Q(\sqrt{161}) \)

• Base field: \(\Q(\sqrt{161}) \)
• Label: 2.2.161.1-10.3-f
• Conductor: 10.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 10.3-f over \(\Q(\sqrt{161}) \)

Isogeny class 10.3-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
10.3-f1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 109403 a - 748767\) , \( -49426978 a + 338292494\bigr] \)
10.3-f2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 5 a - 15\) , \( -16 a + 122\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph