Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-100083.4-a
Conductor 100083.4
Rank \( 1 \)

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 100083.4-a over \(\Q(\sqrt{-3}) \)

Isogeny class 100083.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
100083.4-a1 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 51 a + 166\) , \( -1104 a + 882\bigr] \)
100083.4-a2 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( a + 11\) , \( -13 a + 14\bigr] \)
100083.4-a3 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( a - 4\) , \( -4 a + 2\bigr] \)
100083.4-a4 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -49 a + 96\) , \( 262 a + 94\bigr] \)

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