Properties

Base field 6.6.703493.1
Label 6.6.703493.1-41.4-c
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-c over 6.6.703493.1

Isogeny class 41.4-c contains only one elliptic curve.

Curve label Weierstrass Coefficients
41.4-c1 \( \bigl[a^{5} - 6 a^{3} + a^{2} + 8 a\) , \( -2 a^{5} + 2 a^{4} + 11 a^{3} - 10 a^{2} - 10 a + 4\) , \( a + 1\) , \( 5 a^{5} - a^{4} - 27 a^{3} + 8 a^{2} + 26 a - 1\) , \( -a^{5} + 4 a^{4} + 10 a^{3} - 14 a^{2} - 14 a + 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph