Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-600.1-p
Conductor 600.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 600.1-p over \(\Q(\sqrt{6}) \)

Isogeny class 600.1-p contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
600.1-p1 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -15950 a - 39200\) , \( -1756612 a - 4303380\bigr] \)
600.1-p2 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -400 a - 980\) , \( -59400 a - 145500\bigr] \)
600.1-p3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -400 a + 980\) , \( -1980 a + 4850\bigr] \)
600.1-p4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 100 a - 245\) , \( 0\bigr] \)
600.1-p5 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1000 a - 2450\) , \( 28512 a - 69840\bigr] \)
600.1-p6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
600.1-p7 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 16000 a - 39200\) , \( 1751112 a - 4289340\bigr] \)
600.1-p8 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 15950 a - 39200\) , \( 1756612 a - 4303380\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph