Elliptic curve isogeny class 43.1-b over number field \(\Q(\zeta_{11})^+\)

• Base field: \(\Q(\zeta_{11})^+\)
• Label: 5.5.14641.1-43.1-b
• Conductor: 43.1
• 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 43.1-b over \(\Q(\zeta_{11})^+\)

Isogeny class 43.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
43.1-b1	\( \bigl[a^{3} - 2 a\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} + a - 1\) , \( -273 a^{4} + 380 a^{3} + 846 a^{2} - 1091 a - 235\) , \( 2716 a^{4} - 6086 a^{3} - 5200 a^{2} + 16501 a - 8269\bigr] \)
43.1-b2	\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{4} - a^{3} + 4 a^{2} + 2 a - 2\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{4} - 4 a^{3} + a^{2} + 7 a + 1\) , \( -5 a^{4} - 4 a^{3} + 12 a^{2} + 5 a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph