Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-5000.1-d
Conductor 5000.1
Rank \( 1 \)

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 5000.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 5000.1-d contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
5000.1-d1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -83\) , \( -88\bigr] \)
5000.1-d2 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 709 a - 1238\) , \( -13189 a + 22850\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph