Elliptic curve isogeny class 27.1-a over number field \(\Q(\zeta_{36})^+\)

• Base field: \(\Q(\zeta_{36})^+\)
• Label: 6.6.1259712.1-27.1-a
• Conductor: 27.1
• Rank: \( 0 \)

Base field \(\Q(\zeta_{36})^+\)

Generator \(a\), with minimal polynomial \( x^{6} - 6 x^{4} + 9 x^{2} - 3 \); class number \(1\).

Elliptic curves in class 27.1-a over \(\Q(\zeta_{36})^+\)

Isogeny class 27.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[a^{5} - 5 a^{3} + 5 a\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 3\) , \( a^{4} - 4 a^{2} + a + 2\) , \( 3 a^{5} - 15 a^{3} + 3 a^{2} + 15 a - 3\) , \( -a^{5} - 4 a^{4} + 2 a^{3} + 17 a^{2} - 18\bigr] \)
27.1-a2	\( \bigl[a^{5} - 4 a^{3} + a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 6 a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 3\) , \( -a^{5} + 4 a^{4} + 7 a^{3} - 19 a^{2} - 9 a + 21\) , \( -4 a^{5} + a^{4} + 23 a^{3} - 4 a^{2} - 27 a + 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph