Properties

Base field \(\Q(\sqrt{85}) \)
Label 2.2.85.1-12.1-b
Conductor 12.1
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 12.1-b over \(\Q(\sqrt{85}) \)

Isogeny class 12.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
12.1-b1 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 14 a - 36\) , \( -24 a + 162\bigr] \)
12.1-b2 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 4 a + 14\) , \( 4 a + 16\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph