Properties

Base field 6.6.1868969.1
Label 6.6.1868969.1-34.1-d
Conductor 34.1
Rank bounds 0...1

Related objects

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Base field 6.6.1868969.1

Generator \(a\), with minimal polynomial \( x^{6} - 6 x^{4} - x^{3} + 8 x^{2} + x - 2 \); class number \(1\).

Elliptic curves in class 34.1-d over 6.6.1868969.1

Isogeny class 34.1-d contains only one elliptic curve.

Curve label Weierstrass Coefficients
34.1-d1 \( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} + 3 a - 8\) , \( a^{5} - 5 a^{3} - a^{2} + 5 a + 1\) , \( -3 a^{5} + a^{4} + 13 a^{3} - 8 a + 8\) , \( 15 a^{5} + 13 a^{4} - 71 a^{3} - 78 a^{2} + 18 a + 18\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph