Elliptic curve isogeny class 41.4-d over number field \(\Q(\zeta_{21})^+\)

• Base field: \(\Q(\zeta_{21})^+\)
• Label: 6.6.453789.1-41.4-d
• Conductor: 41.4
• Rank: \( 0 \)

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

Isogeny class 41.4-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
41.4-d1	\( \bigl[a^{5} - 5 a^{3} + a^{2} + 6 a - 2\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 7 a - 4\) , \( a^{2} + a - 2\) , \( -6 a^{5} + 36 a^{3} - 3 a^{2} - 53 a + 7\) , \( -14 a^{5} + 3 a^{4} + 86 a^{3} - 18 a^{2} - 126 a + 18\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph