Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3072.1-g
Conductor 3072.1
Rank \( 0 \)

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 3072.1-g over \(\Q(\sqrt{3}) \)

Isogeny class 3072.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
3072.1-g1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1\) , \( -4 a - 2\bigr] \)
3072.1-g2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -40 a - 56\) , \( 40 a + 72\bigr] \)
3072.1-g3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 36\) , \( -72 a - 120\bigr] \)
3072.1-g4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -320 a - 576\) , \( -4296 a - 7464\bigr] \)

Rank

Rank: \( 0 \)

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