Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-576.7-q
Conductor 576.7
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 576.7-q over \(\Q(\sqrt{17}) \)

Isogeny class 576.7-q contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
576.7-q1 \( \bigl[0\) , \( 1\) , \( a\) , \( 149 a - 397\) , \( -1421 a + 3657\bigr] \)
576.7-q2 \( \bigl[0\) , \( 1\) , \( a\) , \( -a + 3\) , \( -a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph