Elliptic curve isogeny class 196.2-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-196.2-b
• Conductor: 196.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{65}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 16 \); class number \(2\).

Elliptic curves in class 196.2-b over \(\Q(\sqrt{65}) \)

Isogeny class 196.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
196.2-b1	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -42229 a + 191355\) , \( 19886119 a - 90106579\bigr] \)
196.2-b2	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 4841 a - 21925\) , \( -873928 a + 3959869\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph