Properties

Base field \(\Q(\zeta_{11})^+\)
Label 5.5.14641.1-197.1-a
Conductor 197.1
Rank \( 0 \)

Related objects

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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 197.1-a over \(\Q(\zeta_{11})^+\)

Isogeny class 197.1-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
197.1-a1 \( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{4} + 5 a^{2} - a - 4\) , \( a^{4} - 4 a^{2} + 3\) , \( 570 a^{4} - 1045 a^{3} - 1410 a^{2} + 2928 a - 808\) , \( 13157 a^{4} - 24036 a^{3} - 32728 a^{2} + 66751 a - 16212\bigr] \)
197.1-a2 \( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{4} + 5 a^{2} - a - 4\) , \( a^{4} - 4 a^{2} + 3\) , \( -2 a + 2\) , \( -a^{3} + 2 a^{2} + 2 a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph