Elliptic curve isogeny class 149.1-a over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-149.1-a
• Conductor: 149.1
• 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 149.1-a over 4.4.725.1

Isogeny class 149.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
149.1-a1	\( \bigl[1\) , \( -a^{3} + 4 a\) , \( a + 1\) , \( -6 a^{3} - 49 a^{2} + 186 a - 119\) , \( 109 a^{3} - 603 a^{2} + 1020 a - 497\bigr] \)
149.1-a2	\( \bigl[1\) , \( -a^{3} + 4 a\) , \( a + 1\) , \( -a^{3} + a^{2} + a + 1\) , \( -a^{2} + a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph