Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-2100.1-e
Conductor 2100.1
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 2100.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 2100.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
2100.1-e1 \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 2\) , \( -77 a + 217\bigr] \)
2100.1-e2 \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 10 a - 28\) , \( -29 a + 81\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph