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

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

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

Curve label	Weierstrass Coefficients
43.1-a1	\( \bigl[a^{2} + a - 2\) , \( a^{4} - 3 a^{2} - a + 1\) , \( a^{5} + a^{4} - 5 a^{3} - 2 a^{2} + 6 a - 2\) , \( -1815 a^{5} + 640 a^{4} + 11287 a^{3} - 3274 a^{2} - 16592 a + 2508\) , \( 61652 a^{5} - 18037 a^{4} - 382582 a^{3} + 96346 a^{2} + 561130 a - 84717\bigr] \)
43.1-a2	\( \bigl[a^{2} + a - 2\) , \( a^{4} - 3 a^{2} - a + 1\) , \( a^{5} + a^{4} - 5 a^{3} - 2 a^{2} + 6 a - 2\) , \( -3 a^{3} + a^{2} + 8 a - 2\) , \( -a^{5} - a^{4} + 5 a^{3} + 2 a^{2} - 5 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph