Elliptic curve isogeny class 139.1-a over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-139.1-a
• Conductor: 139.1
• 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 139.1-a over 4.4.725.1

Isogeny class 139.1-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
139.1-a1	\( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a\) , \( a^{2}\) , \( -66 a^{3} + 47 a^{2} + 164 a - 120\) , \( -343 a^{3} + 226 a^{2} + 907 a - 665\bigr] \)
139.1-a2	\( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a\) , \( a^{2}\) , \( -a^{3} + 2 a^{2} - a\) , \( -a^{3} + a^{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph