Properties

Base field 4.4.19821.1
Label 4.4.19821.1-9.1-a
Conductor 9.1
Rank not recorded

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Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 9.1-a over 4.4.19821.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 11.

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a\) , \( a^{2} - 4\) , \( 1899 a^{3} - 3107 a^{2} - 25597 a - 9911\) , \( 107727 a^{3} - 331234 a^{2} - 1894883 a - 638778\bigr] \)
9.1-a2 \( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a\) , \( a^{2} - 4\) , \( -a^{3} + 3 a^{2} + 8 a + 4\) , \( 3 a^{3} + 8 a^{2} - 11 a - 3\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph