Elliptic Curve Isogeny Class 85.1-b over Number Field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-85.1-b
• Conductor: 85.1
• 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 85.1-b over 5.5.24217.1

Isogeny class 85.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
85.1-b1	\( \bigl[1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 7 a + 5\) , \( a^{4} - 4 a^{2} + 1\) , \( -182 a^{4} + 70 a^{3} + 883 a^{2} - 144 a - 489\) , \( -1350 a^{4} + 501 a^{3} + 6548 a^{2} - 1077 a - 3642\bigr] \)
85.1-b2	\( \bigl[-2 a^{4} + a^{3} + 10 a^{2} - 2 a - 5\) , \( 3 a^{4} - a^{3} - 14 a^{2} + 3 a + 6\) , \( a^{2} + a - 1\) , \( 4 a^{4} - 19 a^{2} - 3 a + 9\) , \( 4 a^{4} - a^{3} - 19 a^{2} + a + 8\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph