Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-52.2-b
Conductor 52.2
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 52.2-b over \(\Q(\sqrt{3}) \)

Isogeny class 52.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
52.2-b1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -192 a + 334\) , \( 730 a - 1265\bigr] \)
52.2-b2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 28 a - 46\) , \( -126 a + 219\bigr] \)
52.2-b3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 9 a - 12\) , \( -21 a + 37\bigr] \)
52.2-b4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -a - 52\) , \( -63 a - 129\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph