Properties

Base field 4.4.725.1
Label 4.4.725.1-139.3-b
Conductor 139.3
Rank not recorded

Related objects

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Base field 4.4.725.1

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

Elliptic curves in class 139.3-b over 4.4.725.1

Isogeny class 139.3-b contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
139.3-b1 \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - a + 2\) , \( -16 a^{3} - 18 a^{2} + 148 a - 106\) , \( -75 a^{3} - 188 a^{2} + 945 a - 576\bigr] \)
139.3-b2 \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - a + 2\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{3} + a^{2} - a - 1\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph