Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-9.1-b
Conductor 9.1
Rank not recorded

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Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 9.1-b over \(\Q(\sqrt{17}) \)

Isogeny class 9.1-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
9.1-b1 \( \bigl[0\) , \( -a\) , \( 1\) , \( 795 a - 2035\) , \( 17928 a - 45924\bigr] \)
9.1-b2 \( \bigl[0\) , \( -a\) , \( 1\) , \( -5 a + 15\) , \( 2 a - 6\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph