Elliptic curve isogeny class 32.1-a over number field 4.4.6809.1

• Base field: 4.4.6809.1
• Label: 4.4.6809.1-32.1-a
• Conductor: 32.1
• Rank: \( 1 \)

Base field 4.4.6809.1

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

Elliptic curves in class 32.1-a over 4.4.6809.1

Isogeny class 32.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
32.1-a1	\( \bigl[a^{3} - 5 a\) , \( a^{3} + a^{2} - 5 a - 5\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -a^{3} + a^{2} + 9 a + 4\) , \( -3 a^{3} - 12 a^{2} - 14 a - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph