Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-3072.1-d
Conductor 3072.1
Rank \( 1 \)

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Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 3072.1-d over \(\Q(\sqrt{-3}) \)

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

Curve label Weierstrass Coefficients
3072.1-d1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a - 8\) , \( 8\bigr] \)
3072.1-d2 \( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \)
3072.1-d3 \( \bigl[0\) , \( -a\) , \( 0\) , \( -17 a + 17\) , \( -33\bigr] \)
3072.1-d4 \( \bigl[0\) , \( -a\) , \( 0\) , \( -32 a + 32\) , \( 60\bigr] \)

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