Elliptic curve isogeny class 79.4-a over number field \(\Q(\zeta_{13})^+\)

• Base field: \(\Q(\zeta_{13})^+\)
• Label: 6.6.371293.1-79.4-a
• Conductor: 79.4
• 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 \(1\).

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 79.4-a over \(\Q(\zeta_{13})^+\)

Isogeny class 79.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
79.4-a1	\( \bigl[a^{5} - 4 a^{3} + 2 a + 1\) , \( -a^{5} - a^{4} + 4 a^{3} + 5 a^{2} - a - 3\) , \( 1\) , \( -5 a^{5} - 2 a^{4} + 21 a^{3} + 11 a^{2} - 13 a - 3\) , \( -3 a^{5} + a^{4} + 14 a^{3} + 2 a^{2} - 7 a - 1\bigr] \)
79.4-a2	\( \bigl[a^{5} - 4 a^{3} + 2 a + 1\) , \( -a^{5} - a^{4} + 4 a^{3} + 5 a^{2} - a - 3\) , \( 1\) , \( -20 a^{5} - 7 a^{4} + 71 a^{3} + 11 a^{2} - 33 a - 3\) , \( 31 a^{5} + 51 a^{4} - 97 a^{3} - 126 a^{2} + 78 a + 24\bigr] \)