Elliptic curve isogeny class 196.9-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-196.9-b
• Conductor: 196.9
• Rank: \( 0 \)

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

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

Elliptic curves in class 196.9-b over \(\Q(\sqrt{65}) \)

Isogeny class 196.9-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
196.9-b1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 13 a - 57\) , \( 41 a - 182\bigr] \)
196.9-b2	\( \bigl[a\) , \( a\) , \( 0\) , \( 1977 a - 8928\) , \( 180744 a - 818944\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph