Elliptic Curve Isogeny Class 85.2-b over Number Field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-85.2-b
• Conductor: 85.2
• Rank: not recorded

Base field 5.5.24217.1

Generator \(a\), with minimal polynomial \( x^{5} - 5 x^{3} - x^{2} + 3 x + 1 \); class number \(1\).

Elliptic curves in class 85.2-b over 5.5.24217.1

Isogeny class 85.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
85.2-b1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 3 a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( 5 a^{4} - 4 a^{3} - 23 a^{2} + 11 a + 7\) , \( 8 a^{4} - 5 a^{3} - 37 a^{2} + 14 a + 14\bigr] \)
85.2-b2	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 3 a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -50 a^{4} + 26 a^{3} + 232 a^{2} - 74 a - 103\) , \( 65 a^{4} - 10 a^{3} - 330 a^{2} - 4 a + 225\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph