Properties

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

Isogeny class 576.7-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
576.7-f1 \( \bigl[a\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
576.7-f2 \( \bigl[a\) , \( -a\) , \( 0\) , \( -4\) , \( 3 a - 4\bigr] \)
576.7-f3 \( \bigl[a\) , \( -a\) , \( 0\) , \( 15 a - 64\) , \( 84 a - 256\bigr] \)
576.7-f4 \( \bigl[a\) , \( -a\) , \( 0\) , \( -15 a - 24\) , \( 54 a + 72\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph