Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-450.1-f
Conductor 450.1
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 450.1-f over \(\Q(\sqrt{3}) \)

Isogeny class 450.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
450.1-f1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -8\) , \( 11\bigr] \)
450.1-f2 \( \bigl[a\) , \( 0\) , \( 0\) , \( 6\) , \( 0\bigr] \)
450.1-f3 \( \bigl[a\) , \( 0\) , \( 0\) , \( -24\) , \( -18\bigr] \)
450.1-f4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -128\) , \( 587\bigr] \)

Rank

Rank: \( 1 \)

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