Properties

Base field 4.4.2777.1
Label 4.4.2777.1-8.1-a
Conductor 8.1
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 8.1-a over 4.4.2777.1

Isogeny class 8.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
8.1-a1 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a\) , \( a^{2} - a - 1\) , \( 21 a^{3} - 17 a^{2} - 68 a - 26\) , \( 51 a^{3} - 31 a^{2} - 177 a - 87\bigr] \)
8.1-a2 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a\) , \( a^{2} - a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - 2 a^{2} - 2 a + 2\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph