Elliptic curve isogeny class 27.1-a over number field \(\Q(\zeta_{21})^+\)

• Base field: \(\Q(\zeta_{21})^+\)
• Label: 6.6.453789.1-27.1-a
• Conductor: 27.1
• 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 27.1-a over \(\Q(\zeta_{21})^+\)

Isogeny class 27.1-a contains 2 curves linked by isogenies of degree 13.

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[0\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( a^{3} - 2 a\) , \( 652 a^{5} + 912 a^{4} - 2478 a^{3} - 3387 a^{2} + 131 a - 130\) , \( -26388 a^{5} - 27297 a^{4} + 115694 a^{3} + 96838 a^{2} - 65135 a + 8321\bigr] \)
27.1-a2	\( \bigl[0\) , \( -a^{5} + 4 a^{3} - 2 a^{2} - 2 a + 5\) , \( a^{4} - 3 a^{2} + 1\) , \( -2 a^{5} + 7 a^{4} + 4 a^{3} - 28 a^{2} + 17 a + 4\) , \( -6 a^{5} + 13 a^{4} + 15 a^{3} - 52 a^{2} + 33 a - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph