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

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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-745-1.1-c1e2-0-0 Genus 2 curve 745.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $( 1 - T )( 1 + 3 T + 5 T^{2} )$ $1 + 4 T^{2} + 49 T^{4}$
4-29e2-1.1-c1e2-0-1 Elliptic curve 2.2.29.1-1.1-a Hilbert modular form 2.2.29.1-1.1-a Modular form 29.2.b.a $1 + T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $( 1 + 3 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )^{2}$
4-1696-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-106.1-a Bianchi modular form 2.0.4.1-106.2-a Elliptic curve 2.0.4.1-106.1-a Elliptic curve 2.0.4.1-106.2-a Genus 2 curve 1696.b $1 - T$ $1 - T^{2} + 9 T^{4}$ $( 1 + 3 T + 5 T^{2} )^{2}$ $1 - 5 T^{2} + 49 T^{4}$
4-1900-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-76.1-b Elliptic curve 2.2.5.1-76.2-b Hilbert modular form 2.2.5.1-76.1-b Hilbert modular form 2.2.5.1-76.2-b $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-2404-1.1-c1e2-0-0 Genus 2 curve 2404.a $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + T - 4 T^{2} + 7 T^{3} + 49 T^{4}$
4-3625-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-145.1-a Elliptic curve 2.2.5.1-145.2-a Hilbert modular form 2.2.5.1-145.1-a Hilbert modular form 2.2.5.1-145.2-a $1 - 2 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + T$ $1 + 4 T^{2} + 49 T^{4}$
4-3701-1.1-c1e2-0-1 Genus 2 curve 3701.a $1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + T + 9 T^{2} + 5 T^{3} + 25 T^{4}$ $1 + 2 T + 4 T^{2} + 14 T^{3} + 49 T^{4}$
4-4649-1.1-c1e2-0-0 Genus 2 curve 4649.a $1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 3 T + 7 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + T - T^{2} + 7 T^{3} + 49 T^{4}$
4-5248-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-82.1-b Elliptic curve 2.2.8.1-82.2-b Hilbert modular form 2.2.8.1-82.1-b Hilbert modular form 2.2.8.1-82.2-b $1 + T$ $1 - T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-6100-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-244.1-b Elliptic curve 2.2.5.1-244.2-b Hilbert modular form 2.2.5.1-244.1-b Hilbert modular form 2.2.5.1-244.2-b $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-6592-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-103.1-a Elliptic curve 2.2.8.1-103.2-a Hilbert modular form 2.2.8.1-103.1-a Hilbert modular form 2.2.8.1-103.2-a $1 + T + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-6725-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-269.1-a Elliptic curve 2.2.5.1-269.2-a Hilbert modular form 2.2.5.1-269.1-a Hilbert modular form 2.2.5.1-269.2-a $1 + T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 - 3 T + 5 T^{2}$ $1 - 5 T^{2} + 49 T^{4}$
4-7012-1.1-c1e2-0-0 Genus 2 curve 7012.a $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 4 T^{2} + 49 T^{4}$
4-7775-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-311.1-a Elliptic curve 2.2.5.1-311.2-a Hilbert modular form 2.2.5.1-311.1-a Hilbert modular form 2.2.5.1-311.2-a $1 + 2 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 4 T + 5 T^{2}$ $1 - 5 T^{2} + 49 T^{4}$
4-8975-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-359.1-a Elliptic curve 2.2.5.1-359.2-a Hilbert modular form 2.2.5.1-359.1-a Hilbert modular form 2.2.5.1-359.2-a $1 - 2 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-95e2-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-361.2-a Elliptic curve 2.2.5.1-361.3-a Hilbert modular form 2.2.5.1-361.2-a Hilbert modular form 2.2.5.1-361.3-a $1 - 2 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-9088-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-142.1-a Elliptic curve 2.2.8.1-142.2-a Hilbert modular form 2.2.8.1-142.1-a Hilbert modular form 2.2.8.1-142.2-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $1 - 8 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )^{2}$
4-9760-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-610.2-a Bianchi modular form 2.0.4.1-610.3-a Elliptic curve 2.0.4.1-610.2-a Elliptic curve 2.0.4.1-610.3-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $( 1 + T )( 1 + 3 T + 5 T^{2} )$ $1 - 5 T^{2} + 49 T^{4}$
4-9826-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-34.1-a Elliptic curve 2.2.17.1-34.2-a Hilbert modular form 2.2.17.1-34.1-a Hilbert modular form 2.2.17.1-34.2-a $( 1 + T )( 1 + 2 T^{2} )$ $1 - T^{2} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 4 T^{2} + 49 T^{4}$
4-9970-1.1-c1e2-0-0 Genus 2 curve 9970.a $( 1 + T )( 1 + T + 2 T^{2} )$ $1 - T^{2} + 9 T^{4}$ $( 1 + T )( 1 + 5 T^{2} )$ $1 + 3 T + 12 T^{2} + 21 T^{3} + 49 T^{4}$
4-104e2-1.1-c1e2-0-0 Genus 2 curve 10816.e $1 + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 3 T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-11140-1.1-c1e2-0-0 Genus 2 curve 11140.a $1 + 2 T + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $1 + 2 T + 14 T^{3} + 49 T^{4}$
4-11275-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-451.1-c Elliptic curve 2.2.5.1-451.4-c Hilbert modular form 2.2.5.1-451.1-c Hilbert modular form 2.2.5.1-451.4-c $1 + T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 - 3 T + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-11275-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-451.1-a Elliptic curve 2.2.5.1-451.4-a Hilbert modular form 2.2.5.1-451.1-a Hilbert modular form 2.2.5.1-451.4-a $1 - 3 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-11455-1.1-c1e2-0-0 Genus 2 curve 11455.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $( 1 + T )( 1 + 5 T^{2} )$ $( 1 + T + 7 T^{2} )^{2}$
4-11536-1.1-c1e2-0-0 Genus 2 curve 11536.a $1 - T$ $1 - T^{2} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 + T )( 1 + T + 7 T^{2} )$
4-11680-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-730.1-a Bianchi modular form 2.0.4.1-730.4-a Elliptic curve 2.0.4.1-730.1-a Elliptic curve 2.0.4.1-730.4-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $( 1 + T )( 1 - 3 T + 5 T^{2} )$ $1 - 5 T^{2} + 49 T^{4}$
4-11728-1.1-c1e2-0-1 Genus 2 curve 11728.d $1 - T$ $1 - T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-110e2-1.1-c1e2-0-4 Elliptic curve 2.2.5.1-484.1-b Elliptic curve 2.2.5.1-484.1-d Hilbert modular form 2.2.5.1-484.1-b Hilbert modular form 2.2.5.1-484.1-d $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 + T^{2} + 49 T^{4}$
4-12112-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-757.1-a Bianchi modular form 2.0.4.1-757.2-a Elliptic curve 2.0.4.1-757.1-a Elliptic curve 2.0.4.1-757.2-a $1 + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 7 T^{2} )^{2}$
4-12625-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-505.1-b Elliptic curve 2.2.5.1-505.2-b Hilbert modular form 2.2.5.1-505.1-b Hilbert modular form 2.2.5.1-505.2-b $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 - T^{2} + 9 T^{4}$ $1 - T$ $1 - 9 T^{2} + 49 T^{4}$
4-12688-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-793.1-a Bianchi modular form 2.0.4.1-793.4-a Elliptic curve 2.0.4.1-793.1-a Elliptic curve 2.0.4.1-793.4-a $1 + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 - 5 T^{2} + 49 T^{4}$
4-12725-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-509.1-a Elliptic curve 2.2.5.1-509.2-a Hilbert modular form 2.2.5.1-509.1-a Hilbert modular form 2.2.5.1-509.2-a $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 - T^{2} + 9 T^{4}$ $1 + T + 5 T^{2}$ $1 + 2 T^{2} + 49 T^{4}$
4-13132-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-268.3-a Bianchi modular form 2.0.7.1-268.4-a Elliptic curve 2.0.7.1-268.3-a Elliptic curve 2.0.7.1-268.4-a $( 1 + T )^{2}$ $1 - T^{2} + 9 T^{4}$ $1 - 8 T^{2} + 25 T^{4}$ $1 + T + 7 T^{2}$
4-13483-1.1-c1e2-0-0 Genus 2 curve 13483.a $1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 5 T^{2} + 25 T^{4}$ $1 + 2 T + 3 T^{2} + 14 T^{3} + 49 T^{4}$
4-13600-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-850.1-a Bianchi modular form 2.0.4.1-850.6-a Elliptic curve 2.0.4.1-850.1-a Elliptic curve 2.0.4.1-850.6-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-13888-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-217.1-c Elliptic curve 2.2.8.1-217.4-c Hilbert modular form 2.2.8.1-217.1-c Hilbert modular form 2.2.8.1-217.4-c $1 + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $1 - 8 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + T + 7 T^{2} )$
4-14500-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-580.1-a Elliptic curve 2.2.5.1-580.2-a Hilbert modular form 2.2.5.1-580.1-a Hilbert modular form 2.2.5.1-580.2-a $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $1 + T$ $1 + 4 T^{2} + 49 T^{4}$
4-14500-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-580.1-c Elliptic curve 2.2.5.1-580.2-c Hilbert modular form 2.2.5.1-580.1-c Hilbert modular form 2.2.5.1-580.2-c $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $1 - T$ $1 - 8 T^{2} + 49 T^{4}$
4-14731-1.1-c1e2-0-2 Genus 2 curve 14731.c $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 - T - 3 T^{2} - 5 T^{3} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-15028-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-52.3-a Elliptic curve 2.2.17.1-52.6-a Hilbert modular form 2.2.17.1-52.3-a Hilbert modular form 2.2.17.1-52.6-a $1 + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $1 - 8 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-15100-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-604.1-a Elliptic curve 2.2.5.1-604.2-a Hilbert modular form 2.2.5.1-604.1-a Hilbert modular form 2.2.5.1-604.2-a $( 1 - T )( 1 + T )$ $1 - T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 - 5 T^{2} + 49 T^{4}$
4-15121-1.1-c1e2-0-0 Genus 2 curve 15121.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $1 + 9 T^{2} + 49 T^{4}$
4-15232-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-238.2-a Elliptic curve 2.2.8.1-238.3-a Hilbert modular form 2.2.8.1-238.2-a Hilbert modular form 2.2.8.1-238.3-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 - 5 T + 7 T^{2} )$
4-15232-1.1-c1e2-0-5 Elliptic curve 2.2.8.1-238.2-c Elliptic curve 2.2.8.1-238.3-c Hilbert modular form 2.2.8.1-238.2-c Hilbert modular form 2.2.8.1-238.3-c $1 - T$ $1 - T^{2} + 9 T^{4}$ $1 - 8 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + T + 7 T^{2} )$
4-15440-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-965.1-b Bianchi modular form 2.0.4.1-965.4-b Elliptic curve 2.0.4.1-965.1-b Elliptic curve 2.0.4.1-965.4-b $1 + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $( 1 + T )( 1 - 3 T + 5 T^{2} )$ $1 - 5 T^{2} + 49 T^{4}$
4-15760-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-985.1-a Bianchi modular form 2.0.4.1-985.4-a Elliptic curve 2.0.4.1-985.1-a Elliptic curve 2.0.4.1-985.4-a $1 + 2 T + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $( 1 + T )( 1 + T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-16225-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-649.1-c Elliptic curve 2.2.5.1-649.4-c Hilbert modular form 2.2.5.1-649.1-c Hilbert modular form 2.2.5.1-649.4-c $1 + T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-16225-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-649.1-b Elliptic curve 2.2.5.1-649.4-b Hilbert modular form 2.2.5.1-649.1-b Hilbert modular form 2.2.5.1-649.4-b $1 - 3 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 4 T + 5 T^{2}$ $1 + 8 T^{2} + 49 T^{4}$
4-16441-1.1-c1e2-0-0 Genus 2 curve 16441.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 2 T^{2} + 25 T^{4}$ $1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4}$
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