Properties

Base field 4.4.8069.1
Label 4.4.8069.1-16.1-a
Conductor 16.1
Rank \( 1 \)

Related objects

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Base field 4.4.8069.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} + 5 x + 1 \); class number \(1\).

Elliptic curves in class 16.1-a over 4.4.8069.1

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} - 3 a + 1\) , \( -7 a^{3} - 11 a^{2} + 44 a + 11\) , \( -69 a^{3} + a^{2} + 288 a + 49\bigr] \)
16.1-a2 \( \bigl[a^{2} + a - 2\) , \( a^{3} - 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 7 a^{2} + 4 a - 26\) , \( 16 a^{3} - 19 a^{2} - 72 a + 104\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph