Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1.1-a over \(\Q(\sqrt{65}) \)

Isogeny class 1.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[a\) , \( a\) , \( 0\) , \( -11741 a - 41459\) , \( -1744313 a - 6159394\bigr] \)
1.1-a2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 21930 a + 77442\) , \( -5599614 a - 19772961\bigr] \)
1.1-a3	\( \bigl[a\) , \( a\) , \( 0\) , \( -821 a - 2899\) , \( -23499 a - 82978\bigr] \)
1.1-a4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -258 a - 905\) , \( 4597 a + 16233\bigr] \)
1.1-a5	\( \bigl[a\) , \( a\) , \( 0\) , \( -12466 a - 44019\) , \( -1561926 a - 5515362\bigr] \)
1.1-a6	\( \bigl[a\) , \( a\) , \( 0\) , \( -199511 a - 704499\) , \( -98038287 a - 346185826\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph