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

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

Isogeny class 79.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
79.3-a1	\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + a + 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -3 a^{5} - a^{4} + 15 a^{3} + 6 a^{2} - 11 a - 2\) , \( 4 a^{5} + 3 a^{4} - 16 a^{3} - 11 a^{2} + 10 a + 4\bigr] \)
79.3-a2	\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + a + 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 2 a^{5} - 11 a^{4} + 26 a^{2} + 4 a - 7\) , \( -5 a^{5} + 16 a^{4} - 12 a^{3} - 22 a^{2} + 23 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph