Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-50176.2-g
Conductor 50176.2
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 50176.2-g over \(\Q(\sqrt{-3}) \)

Isogeny class 50176.2-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
50176.2-g1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -79 a + 45\) , \( 145 a - 260\bigr] \)
50176.2-g2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 81 a - 35\) , \( 225 a + 80\bigr] \)
50176.2-g3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 15\) , \( 39 a - 12\bigr] \)
50176.2-g4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 260\) , \( 1950 a - 845\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph