Elliptic curve isogeny class 85.1-a over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-85.1-a
• Conductor: 85.1
• 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 85.1-a over 5.5.24217.1

Isogeny class 85.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
85.1-a1	\( \bigl[a^{4} - 4 a^{2}\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 2 a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -31 a^{4} + 10 a^{3} + 150 a^{2} - 19 a - 81\) , \( -59 a^{4} + 21 a^{3} + 287 a^{2} - 44 a - 160\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph