Properties

Base field 6.6.300125.1
Label 6.6.300125.1-71.4-b
Conductor 71.4
Rank \( 1 \)

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 71.4-b over 6.6.300125.1

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

Curve label Weierstrass Coefficients
71.4-b1 \( \bigl[-3 a^{5} + a^{4} + 22 a^{3} + 8 a^{2} - 16 a - 2\) , \( -4 a^{5} + 30 a^{3} + 19 a^{2} - 19 a - 7\) , \( -3 a^{5} + a^{4} + 22 a^{3} + 8 a^{2} - 16 a - 2\) , \( -5 a^{5} + 37 a^{3} + 25 a^{2} - 23 a - 11\) , \( -a^{5} + 7 a^{3} + 6 a^{2} - 4 a - 3\bigr] \)
71.4-b2 \( \bigl[-3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 5\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 21 a - 7\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 23 a^{5} - 17 a^{4} - 160 a^{3} + 3 a^{2} + 116 a - 21\) , \( -39 a^{5} + 37 a^{4} + 268 a^{3} - 63 a^{2} - 227 a + 94\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph