Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-17.1-b
Conductor 17.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 17.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 17.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
17.1-b1 \( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)
17.1-b2 \( \bigl[a\) , \( -a\) , \( 1\) , \( -11 a - 14\) , \( 26 a + 50\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph