Elliptic Curve Isogeny Class 41.5-a over Number Field \(\Q(\zeta_{21})^+\)

• Base field: \(\Q(\zeta_{21})^+\)
• Label: 6.6.453789.1-41.5-a
• Conductor: 41.5
• 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 41.5-a over \(\Q(\zeta_{21})^+\)

Isogeny class 41.5-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
41.5-a1	\( \bigl[a^{5} + a^{4} - 4 a^{3} - 2 a^{2} + 3 a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( a^{5} - 4 a^{3} + a^{2} + 3 a - 2\) , \( 17 a^{5} + 13 a^{4} - 68 a^{3} - 31 a^{2} + 59 a - 8\) , \( 42 a^{5} + 54 a^{4} - 196 a^{3} - 123 a^{2} + 199 a - 27\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph