Properties

Base field 4.4.2777.1
Label 4.4.2777.1-16.1-b
Conductor 16.1
Rank not recorded

Related objects

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Base field 4.4.2777.1

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

Elliptic curves in class 16.1-b over 4.4.2777.1

Isogeny class 16.1-b contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
16.1-b1 \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{2} - a - 1\) , \( 1375 a^{3} - 489 a^{2} - 5280 a - 3053\) , \( 42544 a^{3} - 11186 a^{2} - 169964 a - 97423\bigr] \)
16.1-b2 \( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a\) , \( a\) , \( -4 a^{3} + 7 a^{2} + 11 a - 12\) , \( 3 a^{3} - 3 a^{2} - 7 a + 6\bigr] \)
16.1-b3 \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 3 a^{3} - 3 a^{2} - 10 a + 3\) , \( -a^{3} + a^{2} + 3 a - 1\bigr] \)
16.1-b4 \( \bigl[1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{2} - a - 1\) , \( 559 a^{3} - 1437 a^{2} - 22 a + 670\) , \( 15729 a^{3} - 39584 a^{2} - 3004 a + 20573\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 14 & 2 \\ 7 & 1 & 2 & 14 \\ 14 & 2 & 1 & 7 \\ 2 & 14 & 7 & 1 \end{array}\right)\)

Isogeny graph