Properties

Base field 4.4.8789.1
Label 4.4.8789.1-31.1-a
Conductor 31.1
Rank \( 1 \)

Related objects

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Base field 4.4.8789.1

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

Elliptic curves in class 31.1-a over 4.4.8789.1

Isogeny class 31.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
31.1-a1 \( \bigl[2 a^{3} - 3 a^{2} - 10 a\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a\) , \( 37 a^{3} - 88 a^{2} - 96 a + 12\) , \( 300 a^{3} - 579 a^{2} - 1016 a - 309\bigr] \)
31.1-a2 \( \bigl[2 a^{3} - 3 a^{2} - 10 a\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a\) , \( 7 a^{3} - 13 a^{2} - 31 a + 12\) , \( 2 a^{3} - 8 a^{2} - 3 a + 24\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph