Properties

Base field \(\Q(\sqrt{85}) \)
Label 2.2.85.1-12.2-b
Conductor 12.2
Rank not recorded

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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

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Isogeny matrix

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

Isogeny graph