Properties

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

Isogeny class 43.4-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
43.4-a1 \( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} - 3 a\) , \( -281 a^{4} + 780 a^{3} - 124 a^{2} - 737 a + 173\) , \( -7165 a^{4} + 19524 a^{3} - 4247 a^{2} - 15318 a + 4221\bigr] \)
43.4-a2 \( \bigl[a^{3} - 2 a\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{3} - a^{2} + a + 1\) , \( -a^{4} - a^{3} + 2 a^{2} + a - 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph