Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-99.2-a
Conductor 99.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{5}) \)

Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).

Elliptic curves in class 99.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 99.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
99.2-a1 \( \bigl[1\) , \( -\phi + 1\) , \( \phi\) , \( -196 \phi - 224\) , \( -1961 \phi - 1687\bigr] \)
99.2-a2 \( \bigl[\phi + 1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
99.2-a3 \( \bigl[\phi + 1\) , \( 0\) , \( 0\) , \( 15 \phi - 34\) , \( -48 \phi + 79\bigr] \)
99.2-a4 \( \bigl[\phi + 1\) , \( 0\) , \( 0\) , \( -4\) , \( -3 \phi - 2\bigr] \)
99.2-a5 \( \bigl[\phi + 1\) , \( 0\) , \( 0\) , \( -15 \phi - 54\) , \( -90 \phi - 171\bigr] \)
99.2-a6 \( \bigl[\phi\) , \( 0\) , \( 0\) , \( -3 \phi - 180\) , \( 1251 \phi - 3033\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph