Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-128.2-b
Conductor 128.2
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 128.2-b over \(\Q(\sqrt{17}) \)

Isogeny class 128.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
128.2-b1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 28 a - 71\) , \( -142 a + 364\bigr] \)
128.2-b2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 37 a + 60\) , \( -38 a - 60\bigr] \)
128.2-b3 \( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 7\) , \( 2 a - 6\bigr] \)
128.2-b4 \( \bigl[0\) , \( -a\) , \( 0\) , \( -33 a - 51\) , \( 178 a + 278\bigr] \)
128.2-b5 \( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 127\) , \( 218 a - 606\bigr] \)
128.2-b6 \( \bigl[0\) , \( -a\) , \( 0\) , \( -533 a - 831\) , \( 10078 a + 15738\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph