Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3600.1-k
Conductor 3600.1
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 3600.1-k over \(\Q(\sqrt{3}) \)

Isogeny class 3600.1-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
3600.1-k1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 12\) , \( 18 a\bigr] \)
3600.1-k2 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3\) , \( 0\bigr] \)
3600.1-k3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 42\) , \( -78 a - 135\bigr] \)
3600.1-k4 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -78\) , \( 120 a\bigr] \)

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