Elliptic curve isogeny class 17.1-a over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-17.1-a
• Conductor: 17.1
• 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 17.1-a over 5.5.38569.1

Isogeny class 17.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
17.1-a1	\( \bigl[a^{4} - 4 a^{2} + 1\) , \( -3 a^{4} - a^{3} + 14 a^{2} + 4 a - 8\) , \( a^{4} - 4 a^{2} + a + 2\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} + 6 a + 9\) , \( -a^{4} - 4 a^{3} + 7 a^{2} + 16 a - 12\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph