Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-768.1-j
Conductor 768.1
Rank \( 1 \)

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-j over \(\Q(\sqrt{3}) \)

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

Curve label Weierstrass Coefficients
768.1-j1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 20 a - 34\) , \( 54 a - 104\bigr] \)
768.1-j2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -5980 a + 10358\) , \( -217250 a + 376288\bigr] \)
768.1-j3 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1820 a - 3152\) , \( -30640 a + 53070\bigr] \)
768.1-j4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 242 a - 419\) , \( 2437 a - 4221\bigr] \)
768.1-j5 \( \bigl[0\) , \( -1\) , \( 0\) , \( 25220 a - 43682\) , \( -2876590 a + 4982400\bigr] \)
768.1-j6 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -18 a + 31\) , \( 8073 a - 13983\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph