Elliptic curve isogeny class 73.1-b over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-73.1-b
• Conductor: 73.1
• Rank: \( 0 \)

Base field 5.5.38569.1

Generator \(a\), with minimal polynomial \( x^{5} - 5 x^{3} + 4 x - 1 \); class number \(1\).

Elliptic curves in class 73.1-b over 5.5.38569.1

Isogeny class 73.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
73.1-b1	\( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 4\) , \( -a^{4} - a^{3} + 4 a^{2} + 3 a\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 1\) , \( -2 a^{4} - 2 a^{3} + 8 a^{2} + 6 a - 1\) , \( -a^{4} - a^{3} + 4 a^{2} + 3 a - 1\bigr] \)
73.1-b2	\( \bigl[-a^{4} + 5 a^{2} - 3\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( 1\) , \( -123 a^{4} - 33 a^{3} + 608 a^{2} + 165 a - 453\) , \( -1097 a^{4} - 306 a^{3} + 5403 a^{2} + 1501 a - 3989\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph