Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-75625.1-a
Conductor 75625.1
Rank \( 2 \)

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 75625.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 75625.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
75625.1-a1 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 20 a - 21\) , \( 22\bigr] \)
75625.1-a2 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -105 a + 104\) , \( 272\bigr] \)
75625.1-a3 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -730 a + 729\) , \( -7228\bigr] \)
75625.1-a4 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -1480 a + 1479\) , \( 22272\bigr] \)

Rank

Rank: \( 2 \)

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