Properties

Base field 3.3.316.1
Label 3.3.316.1-16.5-b
Conductor 16.5
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 16.5-b over 3.3.316.1

Isogeny class 16.5-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
16.5-b1 \( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 100434688208 a^{2} - 53161745688 a - 426761105098\) , \( -23577610985047683 a^{2} + 12480020414213596 a + 100184582628814686\bigr] \)
16.5-b2 \( \bigl[a^{2} - 3\) , \( -a - 1\) , \( a + 1\) , \( 213 a^{2} - 108 a - 917\) , \( -2667 a^{2} + 1411 a + 11362\bigr] \)
16.5-b3 \( \bigl[a^{2} - 3\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -109074459285818 a^{2} + 57734919768569 a + 463472706625929\) , \( 1508268935406496095109 a^{2} - 798351754803931876384 a - 6408846675837241310282\bigr] \)
16.5-b4 \( \bigl[a^{2} - 3\) , \( -a^{2} + a + 2\) , \( 0\) , \( 297980666 a^{2} - 157726108 a - 1266161726\) , \( -4093950113647 a^{2} + 2166995673374 a + 17395769388977\bigr] \)
16.5-b5 \( \bigl[a^{2} - 3\) , \( -a^{2} + a + 2\) , \( 0\) , \( 18623821 a^{2} - 9857898 a - 79135231\) , \( -63948294020 a^{2} + 33848892296 a + 271725288464\bigr] \)
16.5-b6 \( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( -41098595441852 a^{2} + 21754167987381 a + 174633707952162\) , \( -893212511727360662557 a^{2} + 472792192035817395818 a + 3795385492745243685734\bigr] \)
16.5-b7 \( \bigl[a + 1\) , \( a + 1\) , \( a^{2} - 3\) , \( 64001862107159 a^{2} - 33877246772437 a - 271952906795303\) , \( 407543787751541638838 a^{2} - 215719683985399604073 a - 1731710829597940478002\bigr] \)
16.5-b8 \( \bigl[a + 1\) , \( a + 1\) , \( a^{2} - 3\) , \( 4217266330899 a^{2} - 2232268991762 a - 17919757326708\) , \( 5637971616536361013 a^{2} - 2984271854928490894 a - 23956533748648438226\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph