Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-17.2-b
Conductor 17.2
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 17.2-b over \(\Q(\sqrt{21}) \)

Isogeny class 17.2-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
17.2-b1 \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
17.2-b2 \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 10 a - 25\) , \( -26 a + 76\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph