Elliptic curve isogeny class 73.1-a over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-73.1-a
• Conductor: 73.1
• Rank: \( 1 \)

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-a over 5.5.38569.1

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

Curve label	Weierstrass Coefficients
73.1-a1	\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( -a\) , \( -a^{4} + 5 a^{2} - 4\bigr] \)
73.1-a2	\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( 15 a^{4} - 10 a^{3} - 50 a^{2} + 34 a - 35\) , \( -66 a^{4} + 65 a^{3} + 225 a^{2} - 234 a + 131\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph