Elliptic curve isogeny class 65.1-a over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-65.1-a
• Conductor: 65.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 65.1-a over \(\Q(\sqrt{65}) \)

Isogeny class 65.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
65.1-a1	\( \bigl[1\) , \( 0\) , \( 0\) , \( 4\) , \( 1\bigr] \)
65.1-a2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
65.1-a3	\( \bigl[a\) , \( -a\) , \( a\) , \( -2 a - 11\) , \( -2 a - 10\bigr] \)
65.1-a4	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 252 a - 1104\) , \( 4279 a - 19344\bigr] \)

Rank

Rank: \( 2 \)

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