Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-74529.6-d
Conductor 74529.6
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

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

Elliptic curves in class 74529.6-d over \(\Q(\sqrt{-3}) \)

Isogeny class 74529.6-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
74529.6-d1 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 4110 a - 3469\) , \( 104374 a - 31759\bigr] \)
74529.6-d2 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -94\) , \( 31 a + 332\bigr] \)
74529.6-d3 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -60 a + 1121\) , \( 17212 a - 10555\bigr] \)
74529.6-d4 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 225 a - 214\) , \( 1915 a - 301\bigr] \)