Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-196.1-e
Conductor 196.1
Rank \( 0 \)

Related objects

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 196.1-e over \(\Q(\sqrt{17}) \)

Isogeny class 196.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
196.1-e1 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 1\) , \( 2 a - 5\bigr] \)
196.1-e2 \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -5 a - 8\) , \( -5 a - 8\bigr] \)