Properties

Base field 5.5.65657.1
Label 5.5.65657.1-29.1-a
Conductor 29.1
Rank not recorded

Related objects

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Base field 5.5.65657.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1 \); class number \(1\).

Elliptic curves in class 29.1-a over 5.5.65657.1

Isogeny class 29.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
29.1-a1 \( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 10 a + 8\) , \( a^{2} - a - 1\) , \( 4 a^{4} - 4 a^{3} - 21 a^{2} + 10 a + 22\) , \( 5 a^{4} - 6 a^{3} - 24 a^{2} + 16 a + 21\bigr] \)
29.1-a2 \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -a^{2} + 3\) , \( a^{3} - 3 a - 1\) , \( -6 a^{4} + 9 a^{3} + 25 a^{2} - 25 a - 16\) , \( 3 a^{4} - 5 a^{3} - 12 a^{2} + 11 a + 8\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph