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e.g. 3,7,19 e.g. F3=1-T,F5=1+T+5T^2

Results (1-50 of 633 matches)

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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-76e2-1.1-c1e2-0-3 Bianchi modular form 2.0.4.1-361.1-a Elliptic curve 2.0.4.1-361.1-a $1 + 2 T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-78e2-1.1-c1e2-0-5 Modular form 78.2.e.a $1 - T + T^{2}$ $1 + T + T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4}$
4-126e2-1.1-c1e2-0-7 Modular form 126.2.h.b $1 - T + T^{2}$ $1 + 3 T + 3 T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - 5 T + 7 T^{2}$
4-17056-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-1066.2-a Bianchi modular form 2.0.4.1-1066.3-a Elliptic curve 2.0.4.1-1066.2-a Elliptic curve 2.0.4.1-1066.3-a $1 + T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - 5 T^{2} + 49 T^{4}$
4-23328-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-1458.1-c Elliptic curve 2.0.4.1-1458.1-c $1 + T$ $1$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-28832-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-1802.2-a Bianchi modular form 2.0.4.1-1802.3-a Elliptic curve 2.0.4.1-1802.2-a Elliptic curve 2.0.4.1-1802.3-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + T^{2} + 49 T^{4}$
4-171e2-1.1-c1e2-0-4 Modular form 171.2.g.a $1 - T - T^{2} - 2 T^{3} + 4 T^{4}$ $1 + 3 T + 3 T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-176e2-1.1-c1e2-0-3 Elliptic curve 2.0.11.1-256.1-CMa Elliptic curve 2.0.11.1-256.1-CMb Elliptic curve 2.2.44.1-16.1-b Hilbert modular form 2.2.44.1-16.1-b Modular form 176.2.e.a $1$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-178e2-1.1-c1e2-0-2 Elliptic curve 2.2.89.1-4.1-a Hilbert modular form 2.2.89.1-4.1-a Modular form 178.2.b.b $( 1 + T )^{2}$ $1 - T^{2} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 7 T^{2} )^{2}$
4-182e2-1.1-c1e2-0-12 Modular form 182.2.g.b $1 - T + T^{2}$ $1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + T + T^{2}$
4-189e2-1.1-c1e2-0-14 Modular form 189.2.s.a $1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4}$ $1$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + 5 T + 7 T^{2}$
4-199e2-1.1-c1e2-0-0 Modular form 199.2.a.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-204e2-1.1-c1e2-0-5 Bianchi modular form 2.0.4.1-2601.2-a Elliptic curve 2.0.4.1-2601.2-a $1 + 2 T^{2}$ $( 1 - T )( 1 + T )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-209e2-1.1-c1e2-0-0 Bianchi modular form 2.0.11.1-361.1-a Elliptic curve 2.0.11.1-361.1-a $( 1 + 2 T^{2} )^{2}$ $( 1 + 2 T + 3 T^{2} )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-44217-1.1-c1e2-0-1 Genus 2 curve 44217.a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T^{2} )$ $( 1 - T )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 + 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-49536-1.1-c1e2-0-2 Elliptic curve 2.2.24.1-86.1-a Elliptic curve 2.2.24.1-86.2-a Hilbert modular form 2.2.24.1-86.1-a Hilbert modular form 2.2.24.1-86.2-a $1 - T$ $1 + 2 T + 3 T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-229e2-1.1-c1e2-0-1 Elliptic curve 2.2.229.1-1.1-a Hilbert modular form 2.2.229.1-1.1-a Modular form 229.2.b.a $1 + T^{2} + 4 T^{4}$ $( 1 - T + 3 T^{2} )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 7 T^{2} )^{2}$
4-231e2-1.1-c1e2-0-7 Modular form 231.2.a.b $1 + T - T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 + T )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T )^{2}$
4-232e2-1.1-c1e2-0-2 Bianchi modular form 2.0.4.1-3364.2-b Elliptic curve 2.0.4.1-3364.2-b $1$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-232e2-1.1-c1e2-0-5 Bianchi modular form 2.0.4.1-3364.2-c Elliptic curve 2.0.4.1-3364.2-c $1$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-57596-1.1-c1e2-0-0 Genus 2 curve 57596.a $1 + 2 T^{2}$ $( 1 - 3 T + 3 T^{2} )( 1 - T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + 2 T + 7 T^{2} )$
4-65219-1.1-c1e2-0-0 Bianchi modular form 2.0.11.1-539.1-b Elliptic curve 2.0.11.1-539.1-b $( 1 + 2 T^{2} )^{2}$ $( 1 - T + 3 T^{2} )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + T )$
4-65664-1.1-c1e2-0-9 Elliptic curve 2.2.24.1-114.1-a Elliptic curve 2.2.24.1-114.2-a Hilbert modular form 2.2.24.1-114.1-a Hilbert modular form 2.2.24.1-114.2-a $1 + T$ $1 - T$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-258e2-1.1-c1e2-0-9 Elliptic curve 2.2.129.1-4.1-a Hilbert modular form 2.2.129.1-4.1-a Modular form 258.2.d.b $( 1 - T )^{2}$ $1 + 3 T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-67473-1.1-c1e2-0-3 Elliptic curve 2.2.21.1-153.1-a Elliptic curve 2.2.21.1-153.2-a Hilbert modular form 2.2.21.1-153.1-a Hilbert modular form 2.2.21.1-153.2-a $1 - T^{2} + 4 T^{4}$ $1$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - T + 7 T^{2}$
4-261e2-1.1-c1e2-0-3 Elliptic curve 2.2.29.1-81.1-a Hilbert modular form 2.2.29.1-81.1-a Modular form 261.2.c.a $1 + T^{2} + 4 T^{4}$ $1$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )^{2}$
4-77372-1.1-c1e2-0-1 Elliptic curve 2.2.29.1-92.1-b Elliptic curve 2.2.29.1-92.2-b Hilbert modular form 2.2.29.1-92.1-b Hilbert modular form 2.2.29.1-92.2-b $( 1 - T )( 1 + T )$ $1 + T^{2} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-286e2-1.1-c1e2-0-4 Modular form 286.2.e.b $1 + T + T^{2}$ $1 + 2 T + T^{2} + 6 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - 2 T - 3 T^{2} - 14 T^{3} + 49 T^{4}$
4-286e2-1.1-c1e2-0-7 Modular form 286.2.e.c $1 + T + T^{2}$ $1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4}$
4-291e2-1.1-c1e2-0-9 Modular form 291.2.a.g $1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4}$ $( 1 + T )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + 3 T + 5 T^{2} + 21 T^{3} + 49 T^{4}$
4-87241-1.1-c1e2-0-0 Genus 2 curve 87241.a $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 - 2 T + 7 T^{2} )$
4-299e2-1.1-c1e2-0-5 Modular form 299.2.e.a $1 + T - T^{2} + 2 T^{3} + 4 T^{4}$ $1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - 2 T - 3 T^{2} - 14 T^{3} + 49 T^{4}$
4-89888-1.1-c1e2-0-3 Bianchi modular form 2.0.4.1-5618.2-f Elliptic curve 2.0.4.1-5618.2-f $1 - T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-89964-1.1-c1e2-0-1 Elliptic curve 2.2.21.1-204.1-a Elliptic curve 2.2.21.1-204.2-a Hilbert modular form 2.2.21.1-204.1-a Hilbert modular form 2.2.21.1-204.2-a $( 1 - T )( 1 + T )$ $1 + T$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + T + 7 T^{2}$
4-93312-1.1-c1e2-0-13 Elliptic curve 2.2.24.1-162.1-a Hilbert modular form 2.2.24.1-162.1-a $1 + T$ $1$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-307e2-1.1-c1e2-0-1 Modular form 307.2.a.e $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $1 + 3 T + 5 T^{2} + 9 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - 5 T + 17 T^{2} - 35 T^{3} + 49 T^{4}$
4-308e2-1.1-c1e2-0-13 Bianchi modular form 2.0.4.1-5929.1-b Elliptic curve 2.0.4.1-5929.1-b $1 + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + T )$
4-312e2-1.1-c1e2-0-26 Modular form 312.2.q.a $1$ $1 + T + T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - 7 T^{2} + 49 T^{4}$
4-312e2-1.1-c1e2-0-35 Modular form 312.2.q.c $1$ $1 - T + T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-109744-1.1-c1e2-0-0 Elliptic curve 2.2.76.1-19.1-b Hilbert modular form 2.2.76.1-19.1-b $1 + 2 T^{2}$ $( 1 + 2 T + 3 T^{2} )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-109744-1.1-c1e2-0-1 Elliptic curve 2.2.76.1-19.1-a Hilbert modular form 2.2.76.1-19.1-a $1 + 2 T^{2}$ $( 1 - 2 T + 3 T^{2} )^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-338e2-1.1-c1e2-0-7 Modular form 338.2.c.a $1 + T + T^{2}$ $1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-338e2-1.1-c1e2-0-8 Modular form 338.2.c.f $1 - T + T^{2}$ $1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4}$
4-342e2-1.1-c1e2-0-22 Modular form 342.2.h.d $1 + T + T^{2}$ $1 - 3 T + 3 T^{2}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-123008-1.1-c1e2-0-6 Elliptic curve 2.2.124.1-8.1-a Elliptic curve 2.2.124.1-8.1-b Hilbert modular form 2.2.124.1-8.1-a Hilbert modular form 2.2.124.1-8.1-b $1$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-358e2-1.1-c1e2-0-0 Modular form 358.2.a.c $( 1 + T )^{2}$ $1 - T + T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )^{2}$
4-129056-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-8066.1-a Bianchi modular form 2.0.4.1-8066.4-a Elliptic curve 2.0.4.1-8066.1-a Elliptic curve 2.0.4.1-8066.4-a $1 - T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - 7 T^{2} )^{2}$
4-364e2-1.1-c1e2-0-11 Modular form 364.2.k.b $1$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 + T + T^{2}$
4-135401-1.1-c1e2-0-0 Elliptic curve 2.2.29.1-161.2-d Elliptic curve 2.2.29.1-161.3-d Hilbert modular form 2.2.29.1-161.2-d Hilbert modular form 2.2.29.1-161.3-d $1 + T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + 4 T + 7 T^{2} )$
4-137376-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-8586.1-a Bianchi modular form 2.0.4.1-8586.2-a Elliptic curve 2.0.4.1-8586.1-a Elliptic curve 2.0.4.1-8586.2-a $1 + T$ $1$ $( 1 - 3 T + 5 T^{2} )^{2}$ $1 - 5 T^{2} + 49 T^{4}$
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