Elliptic curve isogeny class 79.3-b over number field \(\Q(\zeta_{13})^+\)

• Base field: \(\Q(\zeta_{13})^+\)
• Label: 6.6.371293.1-79.3-b
• Conductor: 79.3
• 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 79.3-b over \(\Q(\zeta_{13})^+\)

Isogeny class 79.3-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
79.3-b1	\( \bigl[a^{5} - 5 a^{3} + 5 a\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 4\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -8 a^{5} + 3 a^{4} + 40 a^{3} - 8 a^{2} - 45 a\) , \( 9 a^{5} - 4 a^{4} - 48 a^{3} + 9 a^{2} + 59 a + 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph