Properties

Base field 4.4.8069.1
Label 4.4.8069.1-19.2-a
Conductor 19.2
Rank \( 0 \)

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 19.2-a over 4.4.8069.1

Isogeny class 19.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
19.2-a1 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + 4 a\) , \( a + 1\) , \( 2 a^{2} + 3 a - 2\) , \( -3 a^{3} - 3 a^{2} + 8 a\bigr] \)
19.2-a2 \( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -32 a^{3} - 6 a^{2} + 156 a + 28\) , \( -959 a^{3} - 222 a^{2} + 4527 a + 778\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph