Elliptic curve isogeny class 83.1-b over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-83.1-b
• Conductor: 83.1
• Rank: \( 1 \)

Base field 6.6.434581.1

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

Elliptic curves in class 83.1-b over 6.6.434581.1

Isogeny class 83.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
83.1-b1	\( \bigl[2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 5 a + 1\) , \( -a^{5} + 3 a^{4} + a^{3} - 6 a^{2} + 3 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( 18 a^{5} - 46 a^{4} - 52 a^{3} + 127 a^{2} + 30 a - 51\) , \( 28 a^{5} - 70 a^{4} - 83 a^{3} + 190 a^{2} + 48 a - 80\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph