Elliptic curve isogeny class 73.1-a over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-73.1-a
• Conductor: 73.1
• Rank: \( 0 \)

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-a over 5.5.24217.1

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

Curve label	Weierstrass Coefficients
73.1-a1	\( \bigl[a^{3} - 3 a\) , \( 2 a^{4} - 9 a^{2} + 1\) , \( a^{2} + a - 2\) , \( -2 a^{4} - 4 a^{3} + 13 a^{2} + 18 a - 18\) , \( -30 a^{4} + 5 a^{3} + 152 a^{2} - 104\bigr] \)
73.1-a2	\( \bigl[-2 a^{4} + a^{3} + 10 a^{2} - 2 a - 4\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -5 a^{4} + 5 a^{3} + 22 a^{2} - 17 a - 8\) , \( -a^{4} + 4 a^{2} + a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph