Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1083.1-e
Conductor 1083.1
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 1083.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 1083.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1083.1-e1 \( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \)
1083.1-e2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 84 a - 147\) , \( 585 a - 1014\bigr] \)
1083.1-e3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \)
1083.1-e4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph