Properties

Base field \(\Q(\sqrt{85}) \)
Label 2.2.85.1-3.1-a
Conductor 3.1
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 3.1-a over \(\Q(\sqrt{85}) \)

Isogeny class 3.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
3.1-a1 \( \bigl[a\) , \( a\) , \( 0\) , \( 7 a + 6\) , \( 9 a - 1\bigr] \)
3.1-a2 \( \bigl[a\) , \( a\) , \( 0\) , \( -3 a + 21\) , \( -190\bigr] \)
3.1-a3 \( \bigl[a\) , \( a\) , \( 0\) , \( 177 a - 1059\) , \( 2964 a - 16948\bigr] \)
3.1-a4 \( \bigl[a\) , \( a\) , \( 0\) , \( -148 a - 2394\) , \( -5717 a - 52648\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph