Properties

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

Isogeny class 37632.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
37632.2-d1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 168 a - 64\) , \( -492 a - 332\bigr] \)
37632.2-d2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 888 a - 1164\) , \( 14220 a - 11772\bigr] \)
37632.2-d3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -552 a + 676\) , \( -4116 a - 2940\bigr] \)
37632.2-d4 \( \bigl[0\) , \( -1\) , \( 0\) , \( 168 a - 84\) , \( -324 a - 540\bigr] \)

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