Elliptic curve isogeny class 196.5-j over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-196.5-j
• Conductor: 196.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 196.5-j over \(\Q(\sqrt{65}) \)

Isogeny class 196.5-j contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
196.5-j1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 49 a + 160\) , \( 261 a + 912\bigr] \)
196.5-j2	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -2588 a - 9133\) , \( 58839 a + 207765\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph