Properties

Base field \(\Q(\zeta_{11})^+\)
Label 5.5.14641.1-43.2-b
Conductor 43.2
Rank not recorded

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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 43.2-b over \(\Q(\zeta_{11})^+\)

Isogeny class 43.2-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
43.2-b1 \( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{4} - a^{3} + 3 a^{2} + 4 a + 1\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -6 a^{4} - a^{3} + 20 a^{2} + 4 a - 8\) , \( -6 a^{4} + a^{3} + 23 a^{2} - 3 a - 15\bigr] \)
43.2-b2 \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a\) , \( a^{4} - 4 a^{2} + 2\) , \( 42 a^{4} - 193 a^{3} + 148 a^{2} + 559 a - 755\) , \( 589 a^{4} - 2716 a^{3} + 1086 a^{2} + 7676 a - 7875\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph