Elliptic curve isogeny class 12.2-b over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-12.2-b
• Conductor: 12.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 12.2-b over \(\Q(\sqrt{85}) \)

Isogeny class 12.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12.2-b1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -3 a - 4\) , \( -a + 3\bigr] \)
12.2-b2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13 a - 44\) , \( 37 a + 161\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph