Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1089.1-c
Conductor 1089.1
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 1089.1-c over \(\Q(\sqrt{5}) \)

Isogeny class 1089.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1089.1-c1 \( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \)
1089.1-c2 \( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \)
1089.1-c3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \)
1089.1-c4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph