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Degree Bad \(p\) Root analytic conductor Motivic weight Spectral label
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Columns to display Euler factor constraints
e.g. 3,7,19 e.g. F3=1-T,F5=1+T+5T^2

Results (5 matches)

  displayed columns for results
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
12-475e6-1.1-c1e6-0-3 Modular form 475.2.b.c $1 - 2 T^{2} - 3 T^{4} + 13 T^{6} - 12 T^{8} - 32 T^{10} + 64 T^{12}$ $1 - 12 T^{2} + 68 T^{4} - 245 T^{6} + 612 T^{8} - 972 T^{10} + 729 T^{12}$ $1$ $1 - 28 T^{2} + 392 T^{4} - 3381 T^{6} + 19208 T^{8} - 67228 T^{10} + 117649 T^{12}$
12-1682e6-1.1-c1e6-0-0 Modular form 1682.2.b.g $( 1 + T^{2} )^{3}$ $1 - 12 T^{2} + 68 T^{4} - 245 T^{6} + 612 T^{8} - 972 T^{10} + 729 T^{12}$ $( 1 + 5 T + 21 T^{2} + 51 T^{3} + 105 T^{4} + 125 T^{5} + 125 T^{6} )^{2}$ $( 1 - T + 12 T^{2} - 13 T^{3} + 84 T^{4} - 49 T^{5} + 343 T^{6} )^{2}$
12-4600e6-1.1-c1e6-0-3 Modular form 4600.2.e.s $1$ $1 - 12 T^{2} + 68 T^{4} - 245 T^{6} + 612 T^{8} - 972 T^{10} + 729 T^{12}$ $1$ $1 - 18 T^{2} + 143 T^{4} - 860 T^{6} + 7007 T^{8} - 43218 T^{10} + 117649 T^{12}$
12-6100e6-1.1-c1e6-0-2 Modular form 6100.2.c.f $1$ $1 - 12 T^{2} + 68 T^{4} - 245 T^{6} + 612 T^{8} - 972 T^{10} + 729 T^{12}$ $1$ $1 - 28 T^{2} + 392 T^{4} - 3381 T^{6} + 19208 T^{8} - 67228 T^{10} + 117649 T^{12}$
12-6700e6-1.1-c1e6-0-0 Modular form 6700.2.d.m $1$ $1 - 12 T^{2} + 68 T^{4} - 245 T^{6} + 612 T^{8} - 972 T^{10} + 729 T^{12}$ $1$ $1 - 8 T^{2} + 124 T^{4} - 797 T^{6} + 6076 T^{8} - 19208 T^{10} + 117649 T^{12}$