Properties

Base field 6.6.434581.1
Label 6.6.434581.1-71.4-c
Conductor 71.4
Rank \( 1 \)

Related objects

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Base field 6.6.434581.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 71.4-c over 6.6.434581.1

Isogeny class 71.4-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
71.4-c1 \( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 1\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 2\) , \( 2 a^{5} - 7 a^{4} - 2 a^{3} + 19 a^{2} - 2 a - 6\) , \( -a^{5} + a^{4} + 5 a^{3} - a^{2} - 2 a - 1\bigr] \)
71.4-c2 \( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 4 a + 1\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 2\) , \( -3 a^{5} + 3 a^{4} + 18 a^{3} - 16 a^{2} - 12 a + 9\) , \( 8 a^{5} - 20 a^{4} - 12 a^{3} + 36 a^{2} + 3 a - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph