Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-128.5-a
Conductor 128.5
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 128.5-a over \(\Q(\sqrt{17}) \)

Isogeny class 128.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
128.5-a1 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 3\) , \( a + 3\bigr] \)
128.5-a2 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 9\) , \( -2 a + 3\bigr] \)
128.5-a3 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 47 a - 126\) , \( -221 a + 563\bigr] \)
128.5-a4 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 97 a - 256\) , \( 459 a - 1181\bigr] \)

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