Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-37632.2-e
Conductor 37632.2
Rank \( 1 \)

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-e over \(\Q(\sqrt{-3}) \)

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

Curve label Weierstrass Coefficients
37632.2-e1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -19 a + 113\) , \( -567 a + 210\bigr] \)
37632.2-e2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 7\) , \( 5 a - 10\bigr] \)
37632.2-e3 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 7\) , \( -23 a - 22\bigr] \)
37632.2-e4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 381 a - 127\) , \( -1271 a - 1342\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph