Elliptic curve isogeny class 25.2-c over number field 6.6.1202933.1

• Base field: 6.6.1202933.1
• Label: 6.6.1202933.1-25.2-c
• Conductor: 25.2
• Rank: \( 0 \)

Base field 6.6.1202933.1

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

Elliptic curves in class 25.2-c over 6.6.1202933.1

Isogeny class 25.2-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
25.2-c1	\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 10 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 3 a + 1\) , \( -3 a^{5} + 4 a^{4} + 15 a^{3} - 13 a^{2} - 18 a + 8\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 11 a^{2} - 14 a + 6\bigr] \)
25.2-c2	\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 2 a^{2}\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 3 a + 3\) , \( 121 a^{5} - 71 a^{4} - 571 a^{3} + 57 a^{2} + 137 a - 31\) , \( -4539 a^{5} + 6376 a^{4} + 19518 a^{3} - 18850 a^{2} - 6567 a + 3998\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph