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

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

Isogeny class 79.2-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
79.2-b1	\( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 6 a\) , \( a^{4} - 3 a^{2} + a - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( 9 a^{5} + 7 a^{4} - 35 a^{3} - 27 a^{2} + 16 a + 8\) , \( -16 a^{5} - 8 a^{4} + 71 a^{3} + 45 a^{2} - 37 a - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph