Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-722.1-d
Conductor 722.1
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 722.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 722.1-d contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
722.1-d1 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 3921 a - 6791\) , \( 192134 a - 332786\bigr] \)
722.1-d2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph