Properties

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

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

Curve label Weierstrass Coefficients
37632.2-r1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -460\bigr] \)
37632.2-r2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 6176\) , \( -69388\bigr] \)
37632.2-r3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1664\) , \( -9804\bigr] \)
37632.2-r4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -14624\) , \( 669300\bigr] \)
37632.2-r5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1344\) , \( -19404\bigr] \)
37632.2-r6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -21504\) , \( -1220940\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph