Properties

Base field \(\Q(\sqrt{85}) \)
Label 2.2.85.1-4.1-a
Conductor 4.1
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 4.1-a over \(\Q(\sqrt{85}) \)

Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
4.1-a1 \( \bigl[a\) , \( 0\) , \( a\) , \( -383 a - 1644\) , \( -9842 a - 40758\bigr] \)
4.1-a2 \( \bigl[a\) , \( 0\) , \( a\) , \( 2 a + 6\) , \( a + 3\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph