Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-200.1-a
Conductor 200.1
Rank not recorded

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

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

Elliptic curves in class 200.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 200.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
200.1-a1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 13 a + 25\) , \( -52 a - 91\bigr] \)
200.1-a2 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 10\) , \( -17 a - 30\bigr] \)
200.1-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
200.1-a4 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -107 a - 185\) , \( -892 a - 1545\bigr] \)

Rank

Rank not yet determined.

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