Elliptic Curve Isogeny Class 41.1-b over Number Field \(\Q(\zeta_{21})^+\)

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

Isogeny class 41.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
41.1-b1	\( \bigl[a^{3} - 2 a + 1\) , \( a^{5} - 5 a^{3} + 6 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( 4 a^{5} + 3 a^{4} - 20 a^{3} - 8 a^{2} + 19 a - 4\) , \( 28 a^{5} + 18 a^{4} - 137 a^{3} - 58 a^{2} + 124 a - 19\bigr] \)
41.1-b2	\( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 6 a\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -a^{4} + a^{3} + 2 a^{2} - 4 a + 3\) , \( -a^{4} + 3 a^{2} - a - 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph