Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-512.2-e
Conductor 512.2
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 512.2-e over \(\Q(\sqrt{17}) \)

Isogeny class 512.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
512.2-e1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -8 a + 20\bigr] \)
512.2-e2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -104 a - 168\) , \( 192 a + 304\bigr] \)
512.2-e3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -69 a - 108\) , \( -374 a - 584\bigr] \)
512.2-e4 \( \bigl[0\) , \( -1\) , \( 0\) , \( 768 a - 1968\) , \( 7764 a - 19888\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph