Elliptic curve isogeny class 43.1-b over number field \(\Q(\zeta_{21})^+\)

• Base field: \(\Q(\zeta_{21})^+\)
• Label: 6.6.453789.1-43.1-b
• Conductor: 43.1
• 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 43.1-b over \(\Q(\zeta_{21})^+\)

Isogeny class 43.1-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
43.1-b1	\( \bigl[a^{5} + a^{4} - 5 a^{3} - 2 a^{2} + 6 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 9 a + 2\) , \( 0\) , \( 298 a^{5} - 358 a^{4} - 2027 a^{3} + 1978 a^{2} + 3192 a - 2634\) , \( 22934 a^{5} - 21647 a^{4} - 143434 a^{3} + 125585 a^{2} + 208990 a - 162582\bigr] \)
43.1-b2	\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 9 a + 6\) , \( a^{5} + a^{4} - 5 a^{3} - 2 a^{2} + 6 a - 2\) , \( -2 a^{5} - 2 a^{4} + 9 a^{3} + 4 a^{2} - 8 a + 6\) , \( a^{5} + a^{4} - 5 a^{3} - 5 a^{2} + 3 a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph