Properties

Base field 6.6.300125.1
Label 6.6.300125.1-71.6-c
Conductor 71.6
Rank not recorded

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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 71.6-c over 6.6.300125.1

Isogeny class 71.6-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
71.6-c1 \( \bigl[a + 1\) , \( 5 a^{5} - a^{4} - 36 a^{3} - 18 a^{2} + 21 a + 8\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 6 a^{5} - 2 a^{4} - 43 a^{3} - 15 a^{2} + 29 a + 6\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 16 a^{2} - 17 a - 9\bigr] \)
71.6-c2 \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 19 a - 5\) , \( 7 a^{5} - 3 a^{4} - 49 a^{3} - 16 a^{2} + 32 a + 5\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 19 a - 5\) , \( 259 a^{5} - 67 a^{4} - 1864 a^{3} - 861 a^{2} + 1180 a + 354\) , \( -8418 a^{5} + 2341 a^{4} + 60616 a^{3} + 26921 a^{2} - 39489 a - 11664\bigr] \)
71.6-c3 \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 3\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 4\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 12 a + 4\) , \( 63 a^{5} - 19 a^{4} - 441 a^{3} - 212 a^{2} + 256 a + 75\) , \( 137 a^{5} - 41 a^{4} - 974 a^{3} - 478 a^{2} + 562 a + 170\bigr] \)
71.6-c4 \( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 7 a - 3\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 4\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 12 a + 4\) , \( 83 a^{5} - 79 a^{4} - 516 a^{3} - 117 a^{2} + 306 a + 30\) , \( -75 a^{5} + 338 a^{4} - 891 a^{3} - 920 a^{2} + 793 a + 141\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph