Elliptic Curve Isogeny Class 73.1-b over Number Field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-73.1-b
• Conductor: 73.1
• 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 73.1-b over 5.5.24217.1

Isogeny class 73.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
73.1-b1	\( \bigl[-a^{4} + 5 a^{2} + a - 1\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 5\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( -2 a^{4} + 9 a^{2} - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\bigr] \)
73.1-b2	\( \bigl[-a^{4} + 5 a^{2} + a - 1\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 5\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( -22 a^{4} + 10 a^{3} + 104 a^{2} - 20 a - 57\) , \( 68 a^{4} - 24 a^{3} - 329 a^{2} + 46 a + 178\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph