Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1296.1-e
Conductor 1296.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 1296.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 1296.1-e contains 4 curves linked by isogenies of degrees dividing 27.

Curve label Weierstrass Coefficients
1296.1-e1 \( \bigl[0\) , \( -a\) , \( 0\) , \( -39\) , \( -43 a\bigr] \)
1296.1-e2 \( \bigl[0\) , \( a\) , \( 0\) , \( -39\) , \( 43 a\bigr] \)
1296.1-e3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -6 a\bigr] \)
1296.1-e4 \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 6 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph