Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-45.1-a
Conductor 45.1
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 45.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 45.1-a contains 10 curves linked by isogenies of degrees dividing 32.

Curve label Weierstrass Coefficients
45.1-a1 \( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( -4364 \phi - 7739\) , \( -255406 \phi - 296465\bigr] \)
45.1-a2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)
45.1-a3 \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
45.1-a4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
45.1-a5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
45.1-a6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
45.1-a7 \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)
45.1-a8 \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
45.1-a9 \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
45.1-a10 \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi + 1\) , \( 4364 \phi - 12105\) , \( 243301 \phi - 535402\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 8 & 32 & 16 & 8 & 16 & 4 & 32 & 2 & 4 \\ 8 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 & 8 \\ 32 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 & 32 \\ 16 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 & 16 \\ 8 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 & 8 \\ 16 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 & 16 \\ 4 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 & 4 \\ 32 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 & 32 \\ 2 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 & 2 \\ 4 & 8 & 32 & 16 & 8 & 16 & 4 & 32 & 2 & 1 \end{array}\right)\)

Isogeny graph