Properties

Base field \(\Q(\zeta_{21})^+\)
Label 6.6.453789.1-41.6-b
Conductor 41.6
Rank \( 0 \)

Related objects

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Base field \(\Q(\zeta_{21})^+\)

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 8 x^{2} - 8 x + 1 \); class number \(1\).

Elliptic curves in class 41.6-b over \(\Q(\zeta_{21})^+\)

Isogeny class 41.6-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
41.6-b1 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{5} - 6 a^{3} + 8 a - 1\) , \( a + 1\) , \( a^{5} - 11 a^{3} + 26 a - 3\) , \( -4 a^{5} + 14 a^{4} + 3 a^{3} - 53 a^{2} + 49 a - 8\bigr] \)
41.6-b2 \( \bigl[a^{5} - 4 a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 5\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 4 a^{5} + 7 a^{4} - 15 a^{3} - 27 a^{2} + 9 a + 20\) , \( 6 a^{5} + 11 a^{4} - 21 a^{3} - 39 a^{2} + 10 a + 22\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph