Elliptic Curve Isogeny Class 64.1-b over Number Field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-64.1-b
• Conductor: 64.1
• Rank: not recorded

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 64.1-b over 6.6.485125.1

Isogeny class 64.1-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
64.1-b1	\( \bigl[a^{4} - 4 a^{2} - a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 3 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 4\) , \( -98 a^{5} + 20 a^{4} + 286 a^{3} - 83 a^{2} + 45 a - 74\) , \( -14247 a^{5} - 1644 a^{4} + 52563 a^{3} - 926 a^{2} - 28214 a + 5435\bigr] \)
64.1-b2	\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 7 a - 2\) , \( -2 a^{4} + a^{3} + 7 a^{2} - 3 a\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 6 a + 2\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph