Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-15876.2-d
Conductor 15876.2
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 15876.2-d over \(\Q(\sqrt{-3}) \)

Isogeny class 15876.2-d contains 5 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
15876.2-d1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1062 a\) , \( 13590\bigr] \)
15876.2-d2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -138 a + 330\) , \( 1650 a + 300\bigr] \)
15876.2-d3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12 a\) , \( 24\bigr] \)
15876.2-d4 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -11 a\) , \( 5\bigr] \)
15876.2-d5 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 192 a - 330\) , \( -1650 a + 1950\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph