Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-768.1-n
Conductor 768.1
Rank \( 0 \)

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 768.1-n over \(\Q(\sqrt{3}) \)

Isogeny class 768.1-n contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
768.1-n1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 41\) , \( -11 a - 177\bigr] \)
768.1-n2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 200974 a - 348097\) , \( -64360541 a + 111475727\bigr] \)
768.1-n3 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 12804 a - 22177\) , \( -955655 a + 1655243\bigr] \)
768.1-n4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -43196 a + 74818\) , \( -28011318 a + 48517026\bigr] \)
768.1-n5 \( \bigl[0\) , \( 1\) , \( 0\) , \( 216 a - 374\) , \( 1926 a - 3336\bigr] \)
768.1-n6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -444 a + 766\) , \( 10806 a - 18720\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph