Elliptic curve isogeny class 21.1-a over number field 5.5.149169.1

• Base field: 5.5.149169.1
• Label: 5.5.149169.1-21.1-a
• Conductor: 21.1
• Rank: \( 1 \)

Base field 5.5.149169.1

Generator \(a\), with minimal polynomial \( x^{5} - 6 x^{3} - 3 x^{2} + 4 x + 1 \); class number \(1\).

Elliptic curves in class 21.1-a over 5.5.149169.1

Isogeny class 21.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
21.1-a1	\( \bigl[a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( a^{3} - 4 a - 2\) , \( 1\) , \( -3 a^{4} + a^{3} + 17 a^{2} + 6 a - 8\) , \( -3 a^{4} + 3 a^{3} + 14 a^{2} - a - 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph