Elliptic curve isogeny class 196.4-h over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-196.4-h
• Conductor: 196.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 196.4-h over \(\Q(\sqrt{65}) \)

Isogeny class 196.4-h contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
196.4-h1	\( \bigl[a\) , \( a\) , \( a\) , \( 33766 a - 152979\) , \( -6897995 a + 31255726\bigr] \)
196.4-h2	\( \bigl[a\) , \( a\) , \( a\) , \( -309 a + 1421\) , \( 18531 a - 83938\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph