Elliptic curve isogeny class 79.1-d over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-79.1-d
• Conductor: 79.1
• Rank: \( 0 \)

Base field 6.6.485125.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 8 x^{3} + 2 x^{2} - 5 x + 1 \); class number \(1\).

Elliptic curves in class 79.1-d over 6.6.485125.1

Isogeny class 79.1-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
79.1-d1	\( \bigl[a^{4} - 3 a^{2} + 1\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 11 a^{2} + 4 a - 6\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 1\) , \( 6 a^{5} - a^{4} - 24 a^{3} + 6 a^{2} + 19 a - 4\) , \( 16 a^{5} - 9 a^{4} - 59 a^{3} + 34 a^{2} + 28 a - 8\bigr] \)
79.1-d2	\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( a + 1\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 3\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 8 a^{2} + 10 a - 5\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 3 a - 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph