Elliptic curve isogeny class 53.2-a over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-53.2-a
• Conductor: 53.2
• 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 53.2-a over 5.5.24217.1

Isogeny class 53.2-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
53.2-a1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3 a + 4\) , \( a^{4} - 4 a^{2} + 1\) , \( 3 a^{4} - 3 a^{3} - 14 a^{2} + 8 a + 5\) , \( -3 a^{4} + 2 a^{3} + 13 a^{2} - 7 a - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph