Elliptic curve isogeny class 79.1-f over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-79.1-f
• 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-f over 6.6.485125.1

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

Curve label	Weierstrass Coefficients
79.1-f1	\( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 3\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 11 a^{2} - 12 a + 3\) , \( a^{4} - 4 a^{2} + 3\) , \( 6 a^{5} - 12 a^{4} - 32 a^{3} + 43 a^{2} + 38 a - 16\) , \( -4 a^{5} + 5 a^{4} + 25 a^{3} - 14 a^{2} - 37 a - 4\bigr] \)
79.1-f2	\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 8 a^{2} - 3 a + 6\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 2\) , \( -2 a^{5} + 2 a^{4} + 9 a^{3} - 8 a^{2} - 12 a + 11\) , \( -7 a^{5} + 19 a^{4} + 13 a^{3} - 62 a^{2} + 33 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph