Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-2880.1-d
Conductor 2880.1
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 2880.1-d over \(\Q(\sqrt{5}) \)

Isogeny class 2880.1-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
2880.1-d1 \( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -15 \phi - 45\) , \( 243 \phi + 228\bigr] \)
2880.1-d2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \)
2880.1-d3 \( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \)
2880.1-d4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \)
2880.1-d5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \)
2880.1-d6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
2880.1-d7 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \)
2880.1-d8 \( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 17 \phi - 61\) , \( -259 \phi + 532\bigr] \)

Rank

Rank: \( 1 \)

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