Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-4608.1-be
Conductor 4608.1
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 4608.1-be over \(\Q(\sqrt{3}) \)

Isogeny class 4608.1-be contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
4608.1-be1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 660 a - 1143\) , \( -12144 a + 21034\bigr] \)
4608.1-be2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a - 78\) , \( -153 a + 265\bigr] \)
4608.1-be3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a - 36\) , \( 60 a + 100\bigr] \)
4608.1-be4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a + 207\) , \( -1014 a + 1756\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph