Properties

Base field 6.6.300125.1
Label 6.6.300125.1-71.1-a
Conductor 71.1
Rank \( 0 \)

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 71.1-a over 6.6.300125.1

Isogeny class 71.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
71.1-a1 \( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 12\) , \( a + 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( 17 a^{5} + a^{4} - 130 a^{3} - 87 a^{2} + 99 a + 31\) , \( 13 a^{5} + 10 a^{4} - 112 a^{3} - 119 a^{2} + 104 a + 35\bigr] \)
71.1-a2 \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 7\) , \( -7 a^{5} + 2 a^{4} + 50 a^{3} + 22 a^{2} - 30 a - 10\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 2\) , \( 2 a^{5} + 7 a^{4} - 24 a^{3} - 51 a^{2} + 29 a + 8\) , \( -327 a^{5} + 677 a^{4} + 1538 a^{3} - 2267 a^{2} + 286 a + 277\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph