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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 (3 matches)

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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\) \(F_{ 11 }(T)\) \(F_{ 13 }(T)\) \(F_{ 17 }(T)\) \(F_{ 19 }(T)\) \(F_{ 23 }(T)\) \(F_{ 29 }(T)\) \(F_{ 31 }(T)\) \(F_{ 37 }(T)\) \(F_{ 41 }(T)\) \(F_{ 43 }(T)\) \(F_{ 47 }(T)\)
4-901587-1.1-c1e2-0-0 Genus 2 curve 901587.a $1 + T^{2} + 4 T^{4}$ $( 1 + T )( 1 - 2 T + 3 T^{2} )$ $1 + 2 T + 4 T^{2} + 10 T^{3} + 25 T^{4}$ $1 + T - 3 T^{2} + 7 T^{3} + 49 T^{4}$ $1 + T + 21 T^{2} + 11 T^{3} + 121 T^{4}$ $( 1 - T + 13 T^{2} )( 1 + 3 T + 13 T^{2} )$ $1 + 5 T + 35 T^{2} + 85 T^{3} + 289 T^{4}$ $1 + T + 20 T^{2} + 19 T^{3} + 361 T^{4}$ $1 - 14 T + 89 T^{2} - 322 T^{3} + 529 T^{4}$ $1 + 2 T + 12 T^{2} + 58 T^{3} + 841 T^{4}$ $1 + 3 T + 35 T^{2} + 93 T^{3} + 961 T^{4}$ $1 - 7 T + 82 T^{2} - 259 T^{3} + 1369 T^{4}$ $( 1 - 10 T + 41 T^{2} )( 1 - 2 T + 41 T^{2} )$ $1 - 4 T + 72 T^{2} - 172 T^{3} + 1849 T^{4}$ $1 + 4 T - 7 T^{2} + 188 T^{3} + 2209 T^{4}$
4-919168-1.1-c1e2-0-0 Genus 2 curve 919168.b $1$ $1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4}$ $1 - 2 T + 4 T^{2} - 10 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 + 7 T^{2} )$ $( 1 - 5 T + 11 T^{2} )( 1 + 4 T + 11 T^{2} )$ $1 + T + 15 T^{2} + 13 T^{3} + 169 T^{4}$ $1 - 5 T^{2} + 289 T^{4}$ $1 - 5 T + 29 T^{2} - 95 T^{3} + 361 T^{4}$ $1 - 14 T + 89 T^{2} - 322 T^{3} + 529 T^{4}$ $1 - 14 T^{2} + 841 T^{4}$ $1 - 6 T + 54 T^{2} - 186 T^{3} + 961 T^{4}$ $1 + 12 T + 93 T^{2} + 444 T^{3} + 1369 T^{4}$ $1 + T + 60 T^{2} + 41 T^{3} + 1681 T^{4}$ $( 1 - T )( 1 + 5 T + 43 T^{2} )$ $1 - 7 T + 21 T^{2} - 329 T^{3} + 2209 T^{4}$
4-9700e2-1.1-c1e2-0-1 Modular form 9700.2.a.e $1$ $( 1 + 3 T^{2} )^{2}$ $1$ $1 - 2 T + 9 T^{2} - 14 T^{3} + 49 T^{4}$ $( 1 + 2 T + 11 T^{2} )^{2}$ $1 - 4 T + 6 T^{2} - 52 T^{3} + 169 T^{4}$ $1 + 10 T^{2} + 289 T^{4}$ $( 1 + 2 T + 19 T^{2} )^{2}$ $1 - 14 T + 89 T^{2} - 322 T^{3} + 529 T^{4}$ $( 1 + 29 T^{2} )^{2}$ $1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4}$ $( 1 - 2 T + 37 T^{2} )^{2}$ $( 1 + 4 T + 41 T^{2} )^{2}$ $1 - 4 T + 66 T^{2} - 172 T^{3} + 1849 T^{4}$ $1 + 4 T + 74 T^{2} + 188 T^{3} + 2209 T^{4}$