Elliptic curve isogeny class 53.6-a over number field \(\Q(\zeta_{13})^+\)

• Base field: \(\Q(\zeta_{13})^+\)
• Label: 6.6.371293.1-53.6-a
• Conductor: 53.6
• Rank: \( 1 \)

Base field \(\Q(\zeta_{13})^+\)

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 5 x^{4} + 4 x^{3} + 6 x^{2} - 3 x - 1 \); class number \(1\).

Elliptic curves in class 53.6-a over \(\Q(\zeta_{13})^+\)

Isogeny class 53.6-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
53.6-a1	\( \bigl[a^{5} - 4 a^{3} + 2 a + 1\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a - 1\) , \( a^{4} - 3 a^{2} + 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 3 a + 1\) , \( 0\bigr] \)
53.6-a2	\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 2 a\) , \( a^{5} - 4 a^{3} + a\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{5} + 2 a^{4} - 4 a^{3} - 7 a^{2} + a + 2\) , \( a^{5} - 4 a^{3} + a^{2} + 3 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph