Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-676.1-f
Conductor 676.1
Rank \( 0 \)

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 676.1-f over \(\Q(\sqrt{21}) \)

Isogeny class 676.1-f contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
676.1-f1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \)
676.1-f2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \)
676.1-f3 \( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph