Properties

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

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

Curve label Weierstrass Coefficients
1024.1-i1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 3\) , \( -4 a + 7\bigr] \)
1024.1-i2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 42 a - 73\) , \( -182 a + 315\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph