Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1764.1-e
Conductor 1764.1
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 1764.1-e over \(\Q(\sqrt{5}) \)

Isogeny class 1764.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
1764.1-e1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)
1764.1-e2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \)
1764.1-e3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \)
1764.1-e4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
1764.1-e5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
1764.1-e6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \)

Rank

Rank: \( 1 \)

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