Elliptic curve isogeny class 149.3-a over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-149.3-a
• Conductor: 149.3
• 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 149.3-a over 4.4.725.1

Isogeny class 149.3-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
149.3-a1	\( \bigl[1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - a + 2\) , \( 113 a^{3} - 58 a^{2} - 401 a - 165\) , \( 853 a^{3} - 360 a^{2} - 2945 a - 1234\bigr] \)
149.3-a2	\( \bigl[1\) , \( a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - a + 2\) , \( -2 a^{3} + 2 a^{2} + 4 a\) , \( -2 a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph