Elliptic curve isogeny class 79.2-a over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-79.2-a
• Conductor: 79.2
• Rank: \( 1 \)

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 79.2-a over 6.6.485125.1

Isogeny class 79.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
79.2-a1	\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 2\) , \( 2 a^{5} - a^{4} - 10 a^{3} + 3 a^{2} + 9 a\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 5 a^{5} - 2 a^{4} - 20 a^{3} + 9 a^{2} + 14 a - 2\) , \( 7 a^{5} - a^{4} - 25 a^{3} + 6 a^{2} + 10 a - 2\bigr] \)
79.2-a2	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 10 a^{2} - 6 a + 3\) , \( a^{4} - 4 a^{2} - a + 3\) , \( -55 a^{5} + 72 a^{4} + 267 a^{3} - 253 a^{2} - 278 a + 78\) , \( 230 a^{5} - 305 a^{4} - 1123 a^{3} + 1077 a^{2} + 1178 a - 336\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph