Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-676.1-e
Conductor 676.1
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 676.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 676.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
676.1-e1 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( a - 4\) , \( 2 a - 6\bigr] \)
676.1-e2 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 21 a - 64\) , \( 86 a - 242\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph