Properties

Base field 6.6.300125.1
Label 6.6.300125.1-71.3-a
Conductor 71.3
Rank \( 0 \)

Related objects

Learn more

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 71.3-a over 6.6.300125.1

Isogeny class 71.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
71.3-a1 \( \bigl[a\) , \( -7 a^{5} + 3 a^{4} + 49 a^{3} + 16 a^{2} - 32 a - 5\) , \( -a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 3\) , \( -a^{5} - a^{4} + 9 a^{3} + 8 a^{2} - 4 a - 2\) , \( 2 a^{5} - 10 a^{4} + 2 a^{3} + 30 a^{2} - 16\bigr] \)
71.3-a2 \( \bigl[3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 4\) , \( -2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 11 a - 1\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( -7 a^{5} - 2 a^{4} + 55 a^{3} + 44 a^{2} - 32 a - 25\) , \( 88 a^{5} - 195 a^{4} - 254 a^{3} + 186 a^{2} + 98 a - 25\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph