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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-1.1-b
• 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-b over \(\Q(\sqrt{65}) \)

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

Curve label	Weierstrass Coefficients
1.1-b1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -162 a - 565\) , \( -2952 a - 10428\bigr] \)
1.1-b2	\( \bigl[a\) , \( -1\) , \( a\) , \( 24 a + 80\) , \( -168 a - 596\bigr] \)
1.1-b3	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -12 a - 35\) , \( -48 a - 174\bigr] \)
1.1-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
1.1-b5	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -172 a - 600\) , \( -2667 a - 9422\bigr] \)
1.1-b6	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2742 a - 9675\) , \( -160318 a - 566108\bigr] \)

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