Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-4900.1-b
Conductor 4900.1
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 4900.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 4900.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
4900.1-b1 \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 806 a - 1408\) , \( -16293 a + 28252\bigr] \)
4900.1-b2 \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 6 a - 8\) , \( -43 a + 72\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph