Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-43776.2-b
Conductor 43776.2
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 43776.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 43776.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
43776.2-b1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -383 a + 337\) , \( -659 a + 3120\bigr] \)
43776.2-b2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -68 a + 112\) , \( -272 a - 84\bigr] \)
43776.2-b3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22 a - 53\) , \( 13 a + 195\bigr] \)
43776.2-b4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -23 a + 22\) , \( -20 a + 60\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 4 & 2 \\ 4 & 1 & 4 & 2 \\ 4 & 4 & 1 & 2 \\ 2 & 2 & 2 & 1 \end{array}\right)\)

Isogeny graph