Elliptic curve isogeny class 79.2-a over number field \(\Q(\zeta_{13})^+\)

• Base field: \(\Q(\zeta_{13})^+\)
• Label: 6.6.371293.1-79.2-a
• Conductor: 79.2
• 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 79.2-a over \(\Q(\zeta_{13})^+\)

Isogeny class 79.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
79.2-a1	\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 12 a^{2} - 3 a + 8\) , \( 5 a^{5} - 10 a^{4} - 13 a^{3} + 32 a^{2} - 9 a - 3\bigr] \)
79.2-a2	\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{4} - 4 a^{2} + 2\) , \( -16 a^{5} + 43 a^{4} + 24 a^{3} - 132 a^{2} + 82 a - 7\) , \( 127 a^{5} - 279 a^{4} - 308 a^{3} + 894 a^{2} - 296 a - 82\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph