Properties

Base field \(\Q(\sqrt{89}) \)
Label 2.2.89.1-81.1-a
Conductor 81.1
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 81.1-a over \(\Q(\sqrt{89}) \)

Curve label Weierstrass Coefficients
81.1-a1 \( \bigl[0\) , \( 0\) , \( 1\) , \( -1590 a - 8580\) , \( 92750 a + 359875\bigr] \)
81.1-a2 \( \bigl[0\) , \( 0\) , \( 1\) , \( -14310 a - 77220\) , \( -2504250 a - 9716632\bigr] \)
81.1-a3 \( \bigl[0\) , \( 0\) , \( 1\) , \( 1590 a - 10170\) , \( -92750 a + 452625\bigr] \)
81.1-a4 \( \bigl[0\) , \( 0\) , \( 1\) , \( 14310 a - 91530\) , \( 2504250 a - 12220882\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 267 & 89 & 3 \\ 267 & 1 & 3 & 89 \\ 89 & 3 & 1 & 267 \\ 3 & 89 & 267 & 1 \end{array}\right)\)

Isogeny graph