Properties

Base field 6.6.300125.1
Label 6.6.300125.1-71.5-b
Conductor 71.5
Rank \( 1 \)

Related objects

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Base field 6.6.300125.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 71.5-b over 6.6.300125.1

Isogeny class 71.5-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
71.5-b1 \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 8\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( 10 a^{5} - 2 a^{4} - 69 a^{3} - 40 a^{2} + 49 a + 14\) , \( 12 a^{5} + 4 a^{4} - 100 a^{3} - 51 a^{2} + 68 a + 20\bigr] \)
71.5-b2 \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 2 a + 2\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 4 a^{2} - 10 a - 4\) , \( -2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 8 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph