Elliptic Curve Isogeny Class 41.3-a over Number Field \(\Q(\zeta_{21})^+\)

• Base field: \(\Q(\zeta_{21})^+\)
• Label: 6.6.453789.1-41.3-a
• Conductor: 41.3
• Rank: not recorded

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

Isogeny class 41.3-a contains only one elliptic curve.

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

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph