Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-37632.2-o
Conductor 37632.2
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 37632.2-o over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.2-o contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
37632.2-o1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 3\) , \( 2 a + 14\bigr] \)
37632.2-o2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 112 a - 168\) , \( -688 a + 724\bigr] \)
37632.2-o3 \( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 8\) , \( -8 a + 28\bigr] \)
37632.2-o4 \( \bigl[0\) , \( -a\) , \( 0\) , \( 32 a - 208\) , \( -1152 a - 12\bigr] \)
37632.2-o5 \( \bigl[0\) , \( -a\) , \( 0\) , \( -88 a + 72\) , \( -48 a + 228\bigr] \)
37632.2-o6 \( \bigl[0\) , \( -a\) , \( 0\) , \( 1792 a - 2688\) , \( -44704 a + 44404\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 8 & 4 & 8 \\ 4 & 1 & 2 & 2 & 4 & 2 \\ 2 & 2 & 1 & 4 & 2 & 4 \\ 8 & 2 & 4 & 1 & 8 & 4 \\ 4 & 4 & 2 & 8 & 1 & 8 \\ 8 & 2 & 4 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph