Properties

Base field 3.3.316.1
Label 3.3.316.1-16.2-a
Conductor 16.2
Rank \( 0 \)

Related objects

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Base field 3.3.316.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x + 2 \); class number \(1\).

Elliptic curves in class 16.2-a over 3.3.316.1

Isogeny class 16.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
16.2-a1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 37178 a^{2} - 19692 a - 157999\) , \( 5562481 a^{2} - 2944283 a - 23635709\bigr] \)
16.2-a2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6407 a^{2} + 3208 a + 26891\) , \( 17854891 a^{2} - 9448825 a - 75864197\bigr] \)
16.2-a3 \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a^{2} - 2\) , \( 5718326614 a^{2} - 3026804944 a - 24297973164\) , \( 344200023976745 a^{2} - 182190779570766 a - 1462554275103174\bigr] \)
16.2-a4 \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( -710 a^{2} + 377 a + 3018\) , \( -11698 a^{2} + 6191 a + 49704\bigr] \)
16.2-a5 \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 108 a^{2} - 82 a - 507\) , \( -1006 a^{2} + 425 a + 4083\bigr] \)
16.2-a6 \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -7 a^{2} - 22 a - 17\) , \( -65 a^{2} - 71 a + 85\bigr] \)
16.2-a7 \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -2 a^{2} - 2 a + 3\) , \( -2 a^{2} - 3 a + 1\bigr] \)
16.2-a8 \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -202 a^{2} - 282 a + 153\) , \( -3296 a^{2} - 4399 a + 2863\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph