Properties

Base field 4.4.17609.1
Label 4.4.17609.1-20.1-a
Conductor 20.1
Rank \( 1 \)

Related objects

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Base field 4.4.17609.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 10 x - 1 \); class number \(1\).

Elliptic curves in class 20.1-a over 4.4.17609.1

Isogeny class 20.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
20.1-a1 \( \bigl[a^{3} + a^{2} - 4 a\) , \( -a^{2} - 2 a + 3\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( -a^{2} - a + 3\) , \( 2 a^{3} + a^{2} - 12 a + 2\bigr] \)
20.1-a2 \( \bigl[a^{3} + a^{2} - 4 a\) , \( -a^{2} - 2 a + 3\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( 15 a^{3} + 4 a^{2} - 101 a + 13\) , \( -85 a^{3} - 52 a^{2} + 517 a - 55\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph