Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-1083.1-e
Conductor 1083.1
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 1083.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 1083.1-e contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
1083.1-e1 \( \bigl[0\) , \( a\) , \( 1\) , \( 21952 a - 61463\) , \( -2700411 a + 7538465\bigr] \)
1083.1-e2 \( \bigl[0\) , \( a\) , \( 1\) , \( -98 a + 277\) , \( -861 a + 2405\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph