Elliptic curve isogeny class 17.1-d over number field 5.5.38569.1

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

Isogeny class 17.1-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
17.1-d1	\( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 3 a + 4\) , \( -2 a^{4} - a^{3} + 10 a^{2} + 5 a - 7\) , \( a^{4} - 4 a^{2} + 1\) , \( -2 a^{4} - 2 a^{3} + 9 a^{2} + 8 a - 6\) , \( 3 a^{4} - 15 a^{2} - a + 12\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph