Elliptic curve isogeny class 117.1-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-117.1-b
• Conductor: 117.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 117.1-b over \(\Q(\sqrt{65}) \)

Isogeny class 117.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
117.1-b1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
117.1-b2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \)
117.1-b3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 22\bigr] \)
117.1-b4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -69\) , \( -252\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph