Properties

Base field \(\Q(\zeta_{11})^+\)
Label 5.5.14641.1-43.2-a
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-a over \(\Q(\zeta_{11})^+\)

Isogeny class 43.2-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
43.2-a1 \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( 2 a^{4} + 2 a^{3} - 5 a^{2} - 3 a + 2\) , \( 2 a^{4} + 3 a^{3} - 5 a^{2} - 4 a + 1\bigr] \)
43.2-a2 \( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{4} + 4 a^{2} + a - 3\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -30 a^{4} + 30 a^{3} + 25 a^{2} + 160 a - 215\) , \( -226 a^{4} + 563 a^{3} - 458 a^{2} + 913 a - 1012\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph