Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-484.1-a
Conductor 484.1
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 484.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 484.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
484.1-a1 \( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -78 a - 134\) , \( -475 a - 824\bigr] \)
484.1-a2 \( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 2 a + 6\) , \( -5 a - 8\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph