Elliptic curve isogeny class 61.2-b over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-61.2-b
• Conductor: 61.2
• 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 61.2-b over 5.5.24217.1

Isogeny class 61.2-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
61.2-b1	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( 3 a^{4} - 14 a^{2} - a + 3\) , \( a^{4} - 4 a^{2} + a\) , \( a^{4} - 4 a^{3} - 5 a^{2} + 14 a + 9\) , \( 2 a^{4} + a^{3} - 10 a^{2} - 6 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph