Elliptic curve isogeny class 32.1-a over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-32.1-a
• Conductor: 32.1
• Rank: \( 1 \)

Base field 5.5.70601.1

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

Elliptic curves in class 32.1-a over 5.5.70601.1

Isogeny class 32.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
32.1-a1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a\) , \( 2 a^{4} - a^{3} - 11 a^{2} + a + 6\) , \( -3 a^{3} + 5 a^{2} + 9 a - 9\) , \( -3 a^{4} + a^{3} + 16 a^{2} + 4 a - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph