Properties

Base field \(\Q(\sqrt{89}) \)
Label 2.2.89.1-8.1-a
Conductor 8.1
Rank not recorded

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Base field \(\Q(\sqrt{89}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 22 \); class number \(1\).

Elliptic curves in class 8.1-a over \(\Q(\sqrt{89}) \)

Isogeny class 8.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
8.1-a1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -8316 a + 43371\) , \( 324545 a - 1693155\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph