Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-37632.2-q
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 \(1\).

Rank

Rank: \( 0 \)

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

Elliptic curves in class 37632.2-q over \(\Q(\sqrt{-3}) \)

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

Curve label Weierstrass Coefficients
37632.2-q1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 25 a - 6\) , \( 27 a + 26\bigr] \)
37632.2-q2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 2\bigr] \)
37632.2-q3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -25 a + 19\) , \( -27 a + 53\bigr] \)
37632.2-q4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( 72\bigr] \)