Properties

Base field 6.6.434581.1
Label 6.6.434581.1-29.1-d
Conductor 29.1
Rank not recorded

Related objects

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Base field 6.6.434581.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 29.1-d over 6.6.434581.1

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

Curve label Weierstrass Coefficients
29.1-d1 \( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + 3\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 1\) , \( -a^{5} + 2 a^{4} + 2 a^{3} - a^{2} + 2 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 2 a^{2} - 7 a + 1\bigr] \)
29.1-d2 \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} - 5\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph