Properties

Base field 3.3.316.1
Label 3.3.316.1-16.4-a
Conductor 16.4
Rank \( 0 \)

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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 16.4-a over 3.3.316.1

Isogeny class 16.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
16.4-a1 \( \bigl[a^{2} - 3\) , \( 1\) , \( a + 1\) , \( 623 a^{2} - 449 a - 2863\) , \( 14329 a^{2} - 8700 a - 62909\bigr] \)
16.4-a2 \( \bigl[a^{2} - 3\) , \( 1\) , \( a + 1\) , \( 68 a^{2} - 44 a - 303\) , \( -73 a^{2} + 16 a + 269\bigr] \)
16.4-a3 \( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( 0\) , \( a^{2} + 4 a + 4\) , \( 0\bigr] \)
16.4-a4 \( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( 0\) , \( 11635 a^{2} - 6160 a - 49441\) , \( -979527 a^{2} + 518475 a + 4162139\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph