Properties

Base field 4.4.13676.1
Label 4.4.13676.1-20.1-a
Conductor 20.1
Rank \( 1 \)

Related objects

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Base field 4.4.13676.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 6 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 20.1-a over 4.4.13676.1

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

Curve label Weierstrass Coefficients
20.1-a1 \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{3} - a^{2} + 6 a + 1\) , \( a^{2} - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( 95 a^{3} - 107 a^{2} - 553 a + 737\bigr] \)
20.1-a2 \( \bigl[a^{3} - 4 a + 2\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( 22 a^{3} + 9 a^{2} - 119 a - 15\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph