Properties

Base field 6.6.703493.1
Label 6.6.703493.1-41.4-d
Conductor 41.4
Rank \( 0 \)

Related objects

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Base field 6.6.703493.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 5 x^{4} + 11 x^{3} + 2 x^{2} - 9 x + 1 \); class number \(1\).

Elliptic curves in class 41.4-d over 6.6.703493.1

Isogeny class 41.4-d contains only one elliptic curve.

Curve label Weierstrass Coefficients
41.4-d1 \( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 13 a - 2\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 11 a^{2} - 9 a + 5\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 16 a^{2} - 7 a + 14\) , \( -6 a^{5} + 16 a^{4} + 27 a^{3} - 92 a^{2} - 3 a + 86\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph