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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-196.5-d
• 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-d over \(\Q(\sqrt{65}) \)

Isogeny class 196.5-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
196.5-d1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -148 a + 394\) , \( 3319 a - 13307\bigr] \)
196.5-d2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 281 a - 1328\) , \( -4822 a + 21740\bigr] \)
196.5-d3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 606 a - 7088\) , \( 52874 a - 129268\bigr] \)
196.5-d4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 12 a - 101\) , \( -102 a + 353\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph