Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-676.1-a
Conductor 676.1
Rank not recorded

Related objects

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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 676.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 676.1-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
676.1-a1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \)
676.1-a2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph