Elliptic curve isogeny class 139.2-b over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-139.2-b
• Conductor: 139.2
• Rank: \( 0 \)

Base field 4.4.725.1

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

Elliptic curves in class 139.2-b over 4.4.725.1

Isogeny class 139.2-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
139.2-b1	\( \bigl[a^{2} - 1\) , \( a^{2}\) , \( a^{3} - 3 a\) , \( 66 a^{3} - 29 a^{2} - 246 a - 130\) , \( 469 a^{3} - 262 a^{2} - 1781 a - 797\bigr] \)
139.2-b2	\( \bigl[a^{2} - 1\) , \( a^{2}\) , \( a^{3} - 3 a\) , \( a^{3} + a^{2} - a\) , \( a^{3} + a^{2} - a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph