Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-100.1-e
Conductor 100.1
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 100.1-e over \(\Q(\sqrt{17}) \)

Isogeny class 100.1-e contains 2 curves linked by isogenies of degree 13.

Curve label Weierstrass Coefficients
100.1-e1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -118691 a - 185455\) , \( -31941270 a - 49878411\bigr] \)
100.1-e2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -131 a - 205\) , \( 1758 a + 2745\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph