Elliptic curve isogeny class 3.2-b over number field 4.4.17069.1

• Base field: 4.4.17069.1
• Label: 4.4.17069.1-3.2-b
• Conductor: 3.2
• Rank: \( 0 \)

Base field 4.4.17069.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} - 4 x + 3 \); class number \(1\).

Elliptic curves in class 3.2-b over 4.4.17069.1

Isogeny class 3.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
3.2-b1	\( \bigl[a^{3} - a^{2} - 7 a - 4\) , \( -a^{3} + 3 a^{2} + 4 a - 5\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -a^{3} - a^{2} + 11 a + 17\) , \( -3 a^{3} + 2 a^{2} + 25 a + 17\bigr] \)
3.2-b2	\( \bigl[a^{3} - 2 a^{2} - 4 a\) , \( a^{3} - a^{2} - 7 a - 4\) , \( a^{3} - a^{2} - 6 a - 4\) , \( -5 a^{3} + 13 a^{2} + 20 a - 4\) , \( -2 a^{3} + 10 a^{2} - a - 20\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph