Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1024.1-q
Conductor 1024.1
Rank not recorded

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 1024.1-q over \(\Q(\sqrt{3}) \)

Isogeny class 1024.1-q contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1024.1-q1 \( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 11\) , \( -23 a + 38\bigr] \)
1024.1-q2 \( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( -a\bigr] \)
1024.1-q3 \( \bigl[0\) , \( a\) , \( 0\) , \( -12 a - 20\) , \( 22 a + 38\bigr] \)
1024.1-q4 \( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 11\) , \( -23 a - 38\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph