Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-676.5-h
Conductor 676.5
Rank \( 1 \)

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 676.5-h over \(\Q(\sqrt{17}) \)

Isogeny class 676.5-h contains only one elliptic curve.

Curve label Weierstrass Coefficients
676.5-h1 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( 5 a + 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph