Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1600.1-f
Conductor 1600.1
Rank \( 1 \)

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-f over \(\Q(\sqrt{5}) \)

Isogeny class 1600.1-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
1600.1-f1 \( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 16 \phi - 56\) , \( 1104 \phi + 880\bigr] \)
1600.1-f2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 25 \phi - 28\) , \( 55 \phi - 92\bigr] \)
1600.1-f3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -2\bigr] \)
1600.1-f4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -28\) , \( 48\bigr] \)
1600.1-f5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -25 \phi - 3\) , \( -55 \phi - 37\bigr] \)
1600.1-f6 \( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -14 \phi - 41\) , \( -1089 \phi + 2025\bigr] \)

Rank

Rank: \( 1 \)

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