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

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

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

Isogeny class 79.4-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
79.4-b1	\( \bigl[1\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 3 a + 2\) , \( 4 a^{5} + 5 a^{4} - 19 a^{3} - 20 a^{2} + 14 a + 5\) , \( -29 a^{5} - 20 a^{4} + 127 a^{3} + 87 a^{2} - 82 a - 21\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph