Properties

Base field 4.4.16448.1
Label 4.4.16448.1-22.1-a
Conductor 22.1
Rank \( 0 \)

Related objects

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Base field 4.4.16448.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 2 \); class number \(1\).

Elliptic curves in class 22.1-a over 4.4.16448.1

Isogeny class 22.1-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
22.1-a1 \( \bigl[a^{3} - 2 a^{2} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -30 a^{3} + 60 a^{2} + 125 a - 40\) , \( 40 a^{3} - 23 a^{2} - 573 a - 664\bigr] \)
22.1-a2 \( \bigl[a^{3} - 2 a^{2} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a\) , \( a^{3} - 2 a^{2} - 5 a\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph