Properties

Base field \(\Q(\zeta_{11})^+\)
Label 5.5.14641.1-121.1-a
Conductor 121.1
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 121.1-a over \(\Q(\zeta_{11})^+\)

Isogeny class 121.1-a contains 2 curves linked by isogenies of degree 11.

Curve label Weierstrass Coefficients
121.1-a1 \( \bigl[a^{4} - 3 a^{2} + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{2} + a - 1\) , \( -15 a^{4} + 38 a^{3} - 10 a^{2} - 19 a\) , \( 94 a^{4} - 262 a^{3} + 77 a^{2} + 174 a - 46\bigr] \)
121.1-a2 \( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( 2 a^{4} - 5 a^{3} - 6 a^{2} + 13 a - 1\) , \( 16 a^{4} - 31 a^{3} - 40 a^{2} + 86 a - 22\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph