Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-5000.1-i
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-i over \(\Q(\sqrt{3}) \)

Isogeny class 5000.1-i contains only one elliptic curve.

Curve label Weierstrass Coefficients
5000.1-i1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 125 a + 221\) , \( -2234 a - 3875\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph