Elliptic curve isogeny class 9.3-b over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-9.3-b
• Conductor: 9.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 9.3-b over \(\Q(\sqrt{85}) \)

Isogeny class 9.3-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
9.3-b1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a - 21\) , \( -46 a - 191\bigr] \)
9.3-b2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 3 a + 4\) , \( 2 a + 4\bigr] \)
9.3-b3	\( \bigl[1\) , \( -1\) , \( a\) , \( -1997 a - 8205\) , \( -103494 a - 425341\bigr] \)
9.3-b4	\( \bigl[1\) , \( -1\) , \( a\) , \( -31922 a - 131190\) , \( -6657447 a - 27360595\bigr] \)

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