Properties

Base field \(\Q(\zeta_{21})^+\)
Label 6.6.453789.1-41.4-a
Conductor 41.4
Rank \( 1 \)

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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 41.4-a over \(\Q(\zeta_{21})^+\)

Isogeny class 41.4-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
41.4-a1 \( \bigl[a^{5} + a^{4} - 4 a^{3} - 2 a^{2} + 2 a - 2\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( a^{4} - 4 a^{2} + 2\) , \( 3 a^{5} + a^{4} - 15 a^{3} - 3 a^{2} + 17 a + 1\) , \( 2 a^{5} - 10 a^{3} + 2 a^{2} + 10 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph