Elliptic curve isogeny class 53.2-b over number field 6.6.1292517.1

• Base field: 6.6.1292517.1
• Label: 6.6.1292517.1-53.2-b
• Conductor: 53.2
• Rank: \( 0 \)

Base field 6.6.1292517.1

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

Elliptic curves in class 53.2-b over 6.6.1292517.1

Isogeny class 53.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
53.2-b1	\( \bigl[-a^{3} + a^{2} + 3 a - 2\) , \( -3 a^{5} - a^{4} + 16 a^{3} + 9 a^{2} - 6 a - 3\) , \( a^{5} - 6 a^{3} - a^{2} + 5 a + 1\) , \( -57 a^{5} - 28 a^{4} + 325 a^{3} + 211 a^{2} - 221 a - 90\) , \( -173 a^{5} - 70 a^{4} + 992 a^{3} + 565 a^{2} - 720 a - 260\bigr] \)
53.2-b2	\( \bigl[2 a^{5} + a^{4} - 11 a^{3} - 7 a^{2} + 6 a + 2\) , \( -2 a^{5} + a^{4} + 10 a^{3} - 2 a^{2} - 4 a - 1\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 1\) , \( a^{5} - 6 a^{4} - 3 a^{3} + 28 a^{2} - 4 a - 8\) , \( -4 a^{5} + 4 a^{4} + 18 a^{3} - 15 a^{2} - 4 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph