Elliptic curve isogeny class 41.1-d over number field \(\Q(\zeta_{21})^+\)

• Base field: \(\Q(\zeta_{21})^+\)
• Label: 6.6.453789.1-41.1-d
• Conductor: 41.1
• 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 41.1-d over \(\Q(\zeta_{21})^+\)

Isogeny class 41.1-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
41.1-d1	\( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( -a^{5} + 4 a^{3} - 2 a^{2} - 2 a + 5\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{5} + 3 a^{4} + a^{3} - 14 a^{2} + 10 a + 7\) , \( -a^{5} + 4 a^{4} + 2 a^{3} - 17 a^{2} + 8 a + 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph