Elliptic curve isogeny class 61.1-d over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-61.1-d
• Conductor: 61.1
• Rank: \( 1 \)

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 61.1-d over 5.5.24217.1

Isogeny class 61.1-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
61.1-d1	\( \bigl[0\) , \( -2 a^{4} + a^{3} + 10 a^{2} - 2 a - 5\) , \( a^{4} - 4 a^{2} + a + 1\) , \( 4 a^{4} - a^{3} - 18 a^{2} + 2 a + 6\) , \( -2 a^{4} + 8 a^{2} - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph