Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1024.1-e
Conductor 1024.1
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 1024.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 1024.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1024.1-e1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 6\) , \( -12 a + 20\bigr] \)
1024.1-e2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph