Properties

Base field 6.6.1279733.1
Label 6.6.1279733.1-29.4-a
Conductor 29.4
Rank \( 1 \)

Related objects

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Base field 6.6.1279733.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 6 x^{4} + 10 x^{3} + 10 x^{2} - 11 x - 1 \); class number \(1\).

Elliptic curves in class 29.4-a over 6.6.1279733.1

Isogeny class 29.4-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
29.4-a1 \( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} + 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 7 a^{2} + 3\) , \( a^{4} - a^{3} - 3 a^{2} + a + 1\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 13 a - 6\) , \( a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 5 a + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph