Elliptic curve isogeny class 43.2-a over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-43.2-a
• Conductor: 43.2
• 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 43.2-a over 5.5.38569.1

Isogeny class 43.2-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
43.2-a1	\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a\) , \( -a^{4} + 5 a^{2} - 3\) , \( -438 a^{4} - 108 a^{3} + 2123 a^{2} + 558 a - 1557\) , \( -6146 a^{4} - 1666 a^{3} + 30140 a^{2} + 8257 a - 22182\bigr] \)
43.2-a2	\( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - 4 a^{2} - a + 2\) , \( a^{2} + a - 1\) , \( -a + 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph