Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3600.1-o
Conductor 3600.1
Rank \( 1 \)

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 3600.1-o over \(\Q(\sqrt{3}) \)

Isogeny class 3600.1-o contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
3600.1-o1 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -162\) , \( -1530 a\bigr] \)
3600.1-o2 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 18\) , \( 54 a\bigr] \)
3600.1-o3 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5442\) , \( -13050 a\bigr] \)
3600.1-o4 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -822\) , \( -4650 a\bigr] \)
3600.1-o5 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -222\) , \( 630 a\bigr] \)
3600.1-o6 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -4002\) , \( -56826 a\bigr] \)
3600.1-o7 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -3462\) , \( 44694 a\bigr] \)
3600.1-o8 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -64002\) , \( -3608826 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph