Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-100.1-b
Conductor 100.1
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 100.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 100.1-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
100.1-b1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
100.1-b2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
100.1-b3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
100.1-b4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph