Properties

Base field 3.3.733.1
Label 3.3.733.1-16.3-d
Conductor 16.3
Rank \( 0 \)

Related objects

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Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 16.3-d over 3.3.733.1

Isogeny class 16.3-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
16.3-d1 \( \bigl[a\) , \( a - 1\) , \( a^{2} - 4\) , \( 21 a^{2} + 31 a - 64\) , \( 260 a^{2} + 395 a - 828\bigr] \)
16.3-d2 \( \bigl[a\) , \( a - 1\) , \( a^{2} - 4\) , \( -194 a^{2} - 294 a + 616\) , \( -7553 a^{2} - 11470 a + 23996\bigr] \)
16.3-d3 \( \bigl[a\) , \( -a^{2} + a + 5\) , \( a\) , \( 5575750 a^{2} + 993573 a - 37859656\) , \( 11556551448 a^{2} + 2059308953 a - 78469594148\bigr] \)
16.3-d4 \( \bigl[a\) , \( -a^{2} + a + 5\) , \( a\) , \( 74435 a^{2} + 13263 a - 505416\) , \( 13239011 a^{2} + 2359118 a - 89893596\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph