Elliptic curve isogeny class 43.3-b over number field \(\Q(\zeta_{11})^+\)

• Base field: \(\Q(\zeta_{11})^+\)
• Label: 5.5.14641.1-43.3-b
• Conductor: 43.3
• Rank: \( 0 \)

Base field \(\Q(\zeta_{11})^+\)

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1 \); class number \(1\).

Elliptic curves in class 43.3-b over \(\Q(\zeta_{11})^+\)

Isogeny class 43.3-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
43.3-b1	\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 2 a\) , \( 7 a^{3} - 2 a^{2} - 10 a + 2\) , \( 3 a^{4} + 7 a^{3} - 12 a^{2} - 6 a + 4\bigr] \)
43.3-b2	\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 5 a^{2} + 3\) , \( a^{4} - 4 a^{2} + 2\) , \( -21 a^{4} - 275 a^{3} + 41 a^{2} + 674 a - 204\) , \( -200 a^{4} - 2874 a^{3} + 60 a^{2} + 6329 a - 1829\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph