Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1600.1-a
Conductor 1600.1
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 1600.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 1600.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
1600.1-a1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 865 \phi - 2735\) , \( -22280 \phi + 58190\bigr] \)
1600.1-a2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 40 \phi - 35\) , \( -20 \phi - 190\bigr] \)
1600.1-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -65 \phi + 130\) , \( -680 \phi + 1190\bigr] \)
1600.1-a4 \( \bigl[0\) , \( 0\) , \( 0\) , \( 35 \phi - 70\) , \( -120 \phi + 210\bigr] \)
1600.1-a5 \( \bigl[0\) , \( 0\) , \( 0\) , \( -10 \phi - 10\) , \( -20 \phi - 15\bigr] \)
1600.1-a6 \( \bigl[0\) , \( 0\) , \( 0\) , \( -535 \phi - 535\) , \( 8520 \phi + 6390\bigr] \)
1600.1-a7 \( \bigl[0\) , \( 0\) , \( 0\) , \( -40 \phi + 5\) , \( 20 \phi - 210\bigr] \)
1600.1-a8 \( \bigl[0\) , \( 0\) , \( 0\) , \( -865 \phi - 1870\) , \( 22280 \phi + 35910\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph