Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-1444.2-b
Conductor 1444.2
Rank \( 0 \)

Related objects

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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 1444.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 1444.2-b contains 5 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
1444.2-b1 \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1809 a - 330\) , \( 7600 a + 21674\bigr] \)
1444.2-b2 \( \bigl[a\) , \( 0\) , \( 1\) , \( -1810 a + 1480\) , \( -7600 a + 29274\bigr] \)
1444.2-b3 \( \bigl[a\) , \( 0\) , \( 1\) , \( 15 a\) , \( 22\bigr] \)
1444.2-b4 \( \bigl[a\) , \( 0\) , \( 1\) , \( 85 a\) , \( -2456\bigr] \)
1444.2-b5 \( \bigl[a\) , \( 0\) , \( 1\) , \( -10 a\) , \( 90\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 9 & 9 & 3 \\ 9 & 1 & 9 & 9 & 3 \\ 9 & 9 & 1 & 9 & 3 \\ 9 & 9 & 9 & 1 & 3 \\ 3 & 3 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph