Elliptic curve isogeny class 176.1-b over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-176.1-b
• Conductor: 176.1
• 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 176.1-b over 4.4.725.1

Isogeny class 176.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
176.1-b1	\( \bigl[a^{3} - 2 a\) , \( -a^{3} + 3 a + 1\) , \( a^{3} - 2 a + 1\) , \( 8 a^{3} - 25 a^{2} - 16 a - 9\) , \( 21 a^{3} - 90 a^{2} - 71 a - 19\bigr] \)
176.1-b2	\( \bigl[a^{3} - 2 a\) , \( -a^{3} + 3 a + 1\) , \( a^{3} - 2 a + 1\) , \( -2 a^{3} + 4 a + 1\) , \( -a^{3} + 2 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph