Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-71148.2-d
Conductor 71148.2
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 71148.2-d over \(\Q(\sqrt{-3}) \)

Isogeny class 71148.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
71148.2-d1 \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 4 a - 5\) , \( -4\bigr] \)
71148.2-d2 \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -16 a + 15\) , \( -4\bigr] \)
71148.2-d3 \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -126 a + 125\) , \( 612\bigr] \)
71148.2-d4 \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -226 a + 225\) , \( -1180\bigr] \)

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