Elliptic curve isogeny class 59.3-c over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-59.3-c
• Conductor: 59.3
• 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 59.3-c over 6.6.485125.1

Isogeny class 59.3-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
59.3-c1	\( \bigl[a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 4\) , \( -a^{3} + 2 a - 1\) , \( -a^{2} - a + 1\bigr] \)
59.3-c2	\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 8 a^{2} - 3 a + 5\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 5 a + 3\) , \( -4 a^{5} + 3 a^{4} + 16 a^{3} - 13 a^{2} - 11 a + 9\) , \( -4 a^{5} + 2 a^{4} + 16 a^{3} - 9 a^{2} - 11 a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph