Elliptic curve isogeny class 9.2-b over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-9.2-b
• Conductor: 9.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{85}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 21 \); class number \(2\).

Elliptic curves in class 9.2-b over \(\Q(\sqrt{85}) \)

Isogeny class 9.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
9.2-b1	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -3722 a - 15290\) , \( 215742 a + 886647\bigr] \)
9.2-b2	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -1087 a - 4460\) , \( -40234 a - 165357\bigr] \)
9.2-b3	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -222 a - 905\) , \( 3530 a + 14503\bigr] \)
9.2-b4	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -3547 a - 14570\) , \( 241714 a + 993385\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph