Elliptic curve isogeny class 32.1-a over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-32.1-a
• Conductor: 32.1
• Rank: \( 0 \)

Base field 5.5.65657.1

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

Elliptic curves in class 32.1-a over 5.5.65657.1

Isogeny class 32.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
32.1-a1	\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -3 a^{4} + 4 a^{3} + 8 a^{2} - 5 a - 7\) , \( -a^{4} - 2 a^{3} + 7 a^{2} + a - 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph