Properties

Base field \(\Q(\sqrt{85}) \)
Label 2.2.85.1-9.3-a
Conductor 9.3
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 9.3-a over \(\Q(\sqrt{85}) \)

Isogeny class 9.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
9.3-a1 \( \bigl[1\) , \( -1\) , \( a\) , \( 46 a - 294\) , \( -473 a + 2288\bigr] \)
9.3-a2 \( \bigl[1\) , \( -1\) , \( a\) , \( a - 24\) , \( -5 a + 47\bigr] \)
9.3-a3 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( 0\bigr] \)
9.3-a4 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -4 a - 20\) , \( -29 a - 109\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph