Elliptic curve isogeny class 61.1-a over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-61.1-a
• Conductor: 61.1
• 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 61.1-a over 5.5.24217.1

Isogeny class 61.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
61.1-a1	\( \bigl[a\) , \( -5 a^{4} + 2 a^{3} + 24 a^{2} - 5 a - 11\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 4 a + 3\) , \( 7 a^{4} - a^{3} - 34 a^{2} - 2 a + 16\) , \( -2 a^{4} + 3 a^{3} + 11 a^{2} - 12 a - 15\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph