Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-512.1-f
Conductor 512.1
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 512.1-f over \(\Q(\sqrt{3}) \)

Isogeny class 512.1-f contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
512.1-f1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -69 a + 122\) , \( 1490 a - 2580\bigr] \)
512.1-f2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 8\) , \( 12 a - 20\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph