Elliptic curve isogeny class 16.1-a over number field 5.5.81509.1

• Base field: 5.5.81509.1
• Label: 5.5.81509.1-16.1-a
• Conductor: 16.1
• Rank: \( 0 \)

Base field 5.5.81509.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 5 x - 2 \); class number \(1\).

Elliptic curves in class 16.1-a over 5.5.81509.1

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{4} + 6 a^{2} - 6\) , \( a^{3} - 2 a - 1\) , \( -583 a^{4} + 549 a^{3} + 2605 a^{2} - 836 a - 2545\) , \( -10426 a^{4} + 9362 a^{3} + 47928 a^{2} - 14450 a - 47312\bigr] \)
16.1-a2	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} + 4 a^{2} + 2 a\) , \( a^{4} - 5 a^{2} - a + 3\) , \( -2 a^{4} - a^{3} + 9 a^{2} + 7 a - 3\) , \( a^{4} - 4 a^{3} - a^{2} + 13 a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph