Properties

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

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

Curve label Weierstrass Coefficients
12.1-a1 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -23 a - 92\) , \( -57847 a - 237737\bigr] \)
12.1-a2 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -673 a - 2762\) , \( -23395 a - 96149\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph