Properties

Base field 6.6.1241125.1
Label 6.6.1241125.1-25.2-b
Conductor 25.2
Rank not recorded

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Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 25.2-b over 6.6.1241125.1

Isogeny class 25.2-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
25.2-b1 \( \bigl[-a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -6 a^{5} + 2 a^{4} + 41 a^{3} - a^{2} - 65 a - 23\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( -45 a^{5} + 22 a^{4} + 303 a^{3} - 59 a^{2} - 463 a - 84\) , \( -5610 a^{5} + 2584 a^{4} + 38079 a^{3} - 6320 a^{2} - 58796 a - 12189\bigr] \)
25.2-b2 \( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 6\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -5 a^{5} + a^{4} + 36 a^{3} + 3 a^{2} - 62 a - 25\) , \( -6 a^{5} + a^{4} + 41 a^{3} + 4 a^{2} - 64 a - 27\bigr] \)
25.2-b3 \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( 4 a^{5} - a^{4} - 28 a^{3} - a^{2} + 45 a + 16\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 18\) , \( 4 a^{5} - a^{4} - 48 a^{3} - 8 a^{2} + 139 a + 64\) , \( 5 a^{5} + 11 a^{4} - 60 a^{3} - 66 a^{2} + 162 a + 80\bigr] \)
25.2-b4 \( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 10\) , \( -6 a^{5} + 2 a^{4} + 41 a^{3} - a^{2} - 65 a - 21\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( -2 a^{5} - 3 a^{4} + 18 a^{3} + 16 a^{2} - 36 a - 16\) , \( -2 a^{5} - 2 a^{4} + 17 a^{3} + 16 a^{2} - 40 a - 20\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph