Elliptic curve isogeny class 83.1-b over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-83.1-b
• Conductor: 83.1
• 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 83.1-b over 5.5.24217.1

Isogeny class 83.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
83.1-b1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 1\) , \( a^{3} - 3 a - 1\) , \( -12 a^{4} - 6 a^{3} + 52 a^{2} + 36 a + 6\) , \( 21 a^{4} + 20 a^{3} - 89 a^{2} - 105 a - 26\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph