Properties

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

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

Curve label Weierstrass Coefficients
37632.2-k1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 9 a + 3\) , \( -2 a + 16\bigr] \)
37632.2-k2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -56 a + 168\) , \( 688 a + 36\bigr] \)
37632.2-k3 \( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a + 8\) , \( 8 a + 20\bigr] \)
37632.2-k4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -176 a + 208\) , \( 1152 a - 1164\bigr] \)
37632.2-k5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -16 a - 72\) , \( 48 a + 180\bigr] \)
37632.2-k6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -896 a + 2688\) , \( 44704 a - 300\bigr] \)

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