Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-425.1-a
Conductor 425.1
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 425.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 425.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
425.1-a1 \( \bigl[1\) , \( 1\) , \( 0\) , \( -3\) , \( -22\bigr] \)
425.1-a2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -90 a - 140\) , \( 34 a + 53\bigr] \)
425.1-a3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -8\) , \( -13\bigr] \)
425.1-a4 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 89 a - 229\) , \( -35 a + 88\bigr] \)

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