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

• Base field: \(\Q(\zeta_{11})^+\)
• Label: 5.5.14641.1-43.3-a
• 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-a over \(\Q(\zeta_{11})^+\)

Isogeny class 43.3-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
43.3-a1	\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{4} - 5 a^{2} + a + 4\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 201 a^{4} - 446 a^{3} - 237 a^{2} + 764 a - 199\) , \( -340 a^{4} + 1924 a^{3} - 3845 a^{2} + 2952 a - 615\bigr] \)
43.3-a2	\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 5\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -a^{4} + 8\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph