Properties

Base field \(\Q(\zeta_{11})^+\)
Label 5.5.14641.1-43.4-b
Conductor 43.4
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 43.4-b over \(\Q(\zeta_{11})^+\)

Isogeny class 43.4-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
43.4-b1 \( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( 124 a^{4} + 151 a^{3} - 668 a^{2} - 260 a + 194\) , \( 581 a^{4} + 2293 a^{3} - 4817 a^{2} - 3846 a + 946\bigr] \)
43.4-b2 \( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( -a^{4} + a^{3} + 7 a^{2} - 5 a - 6\) , \( 6 a^{4} - 4 a^{3} - 24 a^{2} + 10 a + 19\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph