Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-676.4-h
Conductor 676.4
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 676.4-h over \(\Q(\sqrt{17}) \)

Isogeny class 676.4-h contains only one elliptic curve.

Curve label Weierstrass Coefficients
676.4-h1 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 7 a - 15\) , \( -11 a + 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph