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

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

Isogeny class 41.5-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
41.5-c1	\( \bigl[a^{5} + a^{4} - 5 a^{3} - 2 a^{2} + 6 a - 1\) , \( a^{5} + a^{4} - 4 a^{3} - 2 a^{2} + 2 a - 1\) , \( a^{4} - 3 a^{2} + 1\) , \( 17 a^{5} + 11 a^{4} - 72 a^{3} - 20 a^{2} + 60 a - 11\) , \( 34 a^{5} + 34 a^{4} - 144 a^{3} - 84 a^{2} + 133 a - 13\bigr] \)
41.5-c2	\( \bigl[a^{5} + a^{4} - 5 a^{3} - 2 a^{2} + 5 a - 1\) , \( -a^{5} + 6 a^{3} - 2 a^{2} - 9 a + 4\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{5} + a^{4} - 5 a^{3} - 5 a^{2} + 4 a + 2\) , \( -4 a^{5} - 2 a^{4} + 20 a^{3} + 6 a^{2} - 19 a + 3\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph