Properties

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

Isogeny class 2880.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
2880.1-b1 \( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -8 \phi - 16\) , \( 116 \phi + 84\bigr] \)
2880.1-b2 \( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 337 \phi - 221\) , \( 1687 \phi - 2436\bigr] \)
2880.1-b3 \( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -23 \phi - 41\) , \( -5 \phi - 60\bigr] \)
2880.1-b4 \( \bigl[0\) , \( 1\) , \( 0\) , \( 17 \phi - 156\) , \( 267 \phi - 1036\bigr] \)
2880.1-b5 \( \bigl[0\) , \( 1\) , \( 0\) , \( 2 \phi - 11\) , \( 10 \phi - 10\bigr] \)
2880.1-b6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -73 \phi - 11\) , \( 265 \phi + 95\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph