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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 \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-2714-1.1-c1e2-0-0 Genus 2 curve 2714.a $( 1 + T )( 1 + 2 T^{2} )$ $1 + T + T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 + T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-5024-1.1-c1e2-0-0 Genus 2 curve 5024.b $1 + T$ $1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-5024-1.1-c1e2-0-2 Bianchi modular form 2.0.4.1-314.1-a Bianchi modular form 2.0.4.1-314.2-a Elliptic curve 2.0.4.1-314.1-a Elliptic curve 2.0.4.1-314.2-a $1 + T$ $1 + T^{2} + 9 T^{4}$ $( 1 + 3 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-5125-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-205.1-a Elliptic curve 2.2.5.1-205.2-a Hilbert modular form 2.2.5.1-205.1-a Hilbert modular form 2.2.5.1-205.2-a $1 - 3 T^{2} + 4 T^{4}$ $1 + 4 T^{2} + 9 T^{4}$ $1 + T$ $1 - 4 T^{2} + 49 T^{4}$
4-6950-1.1-c1e2-0-2 Genus 2 curve 6950.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + T + 3 T^{2} + 3 T^{3} + 9 T^{4}$ $1 + 4 T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-9810-1.1-c1e2-0-0 Genus 2 curve 9810.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + 3 T + 3 T^{2}$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-9875-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-395.1-a Elliptic curve 2.2.5.1-395.2-a Hilbert modular form 2.2.5.1-395.1-a Hilbert modular form 2.2.5.1-395.2-a $1 - T^{2} + 4 T^{4}$ $1 - 4 T^{2} + 9 T^{4}$ $1 + T$ $1 - 4 T^{2} + 49 T^{4}$
4-10832-1.1-c1e2-0-0 Genus 2 curve 10832.a $1 + T$ $1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
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 $1 - 3 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-11391-1.1-c1e2-0-0 Genus 2 curve 11391.b $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + 2 T + 3 T^{2} )$ $1 + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-11875-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-475.1-b Elliptic curve 2.2.5.1-475.2-b Hilbert modular form 2.2.5.1-475.1-b Hilbert modular form 2.2.5.1-475.2-b $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1$ $1 - 4 T^{2} + 49 T^{4}$
4-12633-1.1-c1e2-0-0 Genus 2 curve 12633.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + 3 T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-13040-1.1-c1e2-0-1 Genus 2 curve 13040.c $1$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-13100-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-524.1-a Elliptic curve 2.2.5.1-524.2-a Hilbert modular form 2.2.5.1-524.1-a Hilbert modular form 2.2.5.1-524.2-a $1 + T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 3 T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-13147-1.1-c1e2-0-1 Genus 2 curve 13147.b $1 + 2 T^{2} + 4 T^{4}$ $1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-13900-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-556.1-a Elliptic curve 2.2.5.1-556.2-a Hilbert modular form 2.2.5.1-556.1-a Hilbert modular form 2.2.5.1-556.2-a $1 + T^{2}$ $1 + 3 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-14034-1.1-c1e2-0-0 Genus 2 curve 14034.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + 3 T + 3 T^{2} )$ $1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-14073-1.1-c1e2-0-0 Genus 2 curve 14073.a $1 + T + 2 T^{3} + 4 T^{4}$ $( 1 + T )( 1 - T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-14352-1.1-c1e2-0-1 Genus 2 curve 14352.a $1 + T + 2 T^{2}$ $( 1 - T )( 1 + 3 T + 3 T^{2} )$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-14752-1.1-c1e2-0-0 Genus 2 curve 14752.a $1 + 2 T + 2 T^{2}$ $( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 + 5 T + 13 T^{2} + 25 T^{3} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-14988-1.1-c1e2-0-0 Genus 2 curve 14988.a $1 + T + 2 T^{2}$ $( 1 + T )( 1 - T + 3 T^{2} )$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-15028-1.1-c1e2-0-5 Elliptic curve 2.2.17.1-52.3-b Elliptic curve 2.2.17.1-52.6-b Hilbert modular form 2.2.17.1-52.3-b Hilbert modular form 2.2.17.1-52.6-b $1 + 2 T + 2 T^{2}$ $1 + 3 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-15392-1.1-c1e2-0-2 Bianchi modular form 2.0.4.1-962.1-b Bianchi modular form 2.0.4.1-962.4-b Elliptic curve 2.0.4.1-962.1-b Elliptic curve 2.0.4.1-962.4-b $1 - T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 + 3 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-15488-1.1-c1e2-0-4 Genus 2 curve 15488.c $1 - T$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-17104-1.1-c1e2-0-1 Genus 2 curve 17104.b $1 + T$ $1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4}$ $1 + 3 T + 7 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-17775-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-711.1-b Elliptic curve 2.2.5.1-711.2-b Hilbert modular form 2.2.5.1-711.1-b Hilbert modular form 2.2.5.1-711.2-b $1 + 2 T^{2} + 4 T^{4}$ $1 + T^{2}$ $1 + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-18125-1.1-c1e2-0-4 Elliptic curve 2.2.5.1-725.1-c Elliptic curve 2.2.5.1-725.2-c Hilbert modular form 2.2.5.1-725.1-c Hilbert modular form 2.2.5.1-725.2-c $1 + 2 T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1$ $1 - 4 T^{2} + 49 T^{4}$
4-18320-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-1145.2-a Bianchi modular form 2.0.4.1-1145.3-a Elliptic curve 2.0.4.1-1145.2-a Elliptic curve 2.0.4.1-1145.3-a $1 - 2 T + 2 T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - T )( 1 - 2 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-136e2-1.1-c1e2-0-4 Elliptic curve 2.2.17.1-64.2-a Elliptic curve 2.2.17.1-64.3-a Hilbert modular form 2.2.17.1-64.2-a Hilbert modular form 2.2.17.1-64.3-a $1$ $1 + 4 T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-19689-1.1-c1e2-0-0 Genus 2 curve 19689.a $1 + T + 2 T^{3} + 4 T^{4}$ $( 1 - T )( 1 + T + 3 T^{2} )$ $( 1 + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-20386-1.1-c1e2-0-0 Genus 2 curve 20386.a $( 1 + T )( 1 + 2 T^{2} )$ $1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-21248-1.1-c1e2-0-2 Bianchi modular form 2.0.8.1-332.1-a Bianchi modular form 2.0.8.1-332.2-a Elliptic curve 2.0.8.1-332.1-a Elliptic curve 2.0.8.1-332.2-a $1$ $( 1 + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 2 T^{2} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-21375-1.1-c1e2-0-3 Elliptic curve 2.2.5.1-855.1-e Elliptic curve 2.2.5.1-855.2-e Hilbert modular form 2.2.5.1-855.1-e Hilbert modular form 2.2.5.1-855.2-e $1 - 3 T^{2} + 4 T^{4}$ $( 1 - T )( 1 + T )$ $1 - T$ $1 - 4 T^{2} + 49 T^{4}$
4-21725-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-869.1-a Elliptic curve 2.2.5.1-869.4-a Hilbert modular form 2.2.5.1-869.1-a Hilbert modular form 2.2.5.1-869.4-a $1 + T^{2} + 4 T^{4}$ $1 + 4 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-21801-1.1-c1e2-0-0 Elliptic curve 2.2.13.1-129.1-b Elliptic curve 2.2.13.1-129.4-b Hilbert modular form 2.2.13.1-129.1-b Hilbert modular form 2.2.13.1-129.4-b $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $( 1 - T )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-24475-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-979.2-a Elliptic curve 2.2.5.1-979.3-a Hilbert modular form 2.2.5.1-979.2-a Hilbert modular form 2.2.5.1-979.3-a $1 - 3 T^{2} + 4 T^{4}$ $1 - 4 T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-25625-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-1025.1-e Elliptic curve 2.2.5.1-1025.2-e Hilbert modular form 2.2.5.1-1025.1-e Hilbert modular form 2.2.5.1-1025.2-e $1 - T^{2} + 4 T^{4}$ $1 + 4 T^{2} + 9 T^{4}$ $1$ $1 - 4 T^{2} + 49 T^{4}$
4-25632-1.1-c1e2-0-4 Bianchi modular form 2.0.4.1-1602.1-c Bianchi modular form 2.0.4.1-1602.2-c Elliptic curve 2.0.4.1-1602.1-c Elliptic curve 2.0.4.1-1602.2-c $1 - T$ $1 + T^{2}$ $( 1 + 2 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-26725-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-1069.1-a Elliptic curve 2.2.5.1-1069.2-a Hilbert modular form 2.2.5.1-1069.1-a Hilbert modular form 2.2.5.1-1069.2-a $1 - 3 T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-165e2-1.1-c1e2-0-7 Bianchi modular form 2.0.11.1-225.3-b Bianchi modular form 2.0.11.1-225.7-b Elliptic curve 2.0.11.1-225.3-b Elliptic curve 2.0.11.1-225.7-b $1 - T^{2} + 4 T^{4}$ $1 - T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-29525-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-1181.1-a Elliptic curve 2.2.5.1-1181.2-a Hilbert modular form 2.2.5.1-1181.1-a Hilbert modular form 2.2.5.1-1181.2-a $1 + T^{2} + 4 T^{4}$ $1 + 4 T^{2} + 9 T^{4}$ $1 - T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-30400-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-1216.1-b Elliptic curve 2.2.5.1-1216.2-b Hilbert modular form 2.2.5.1-1216.1-b Hilbert modular form 2.2.5.1-1216.2-b $1$ $1 - T^{2} + 9 T^{4}$ $1 - T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-30825-1.1-c1e2-0-0 Genus 2 curve 30825.a $1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T^{2}$ $1 + T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-30927-1.1-c1e2-0-2 Elliptic curve 2.2.13.1-183.1-a Elliptic curve 2.2.13.1-183.4-a Hilbert modular form 2.2.13.1-183.1-a Hilbert modular form 2.2.13.1-183.4-a $1 + T^{2} + 4 T^{4}$ $( 1 + T )( 1 + 3 T^{2} )$ $1 + 2 T^{2} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-31104-1.1-c1e2-0-0 Elliptic curve 2.2.12.1-216.1-b Elliptic curve 2.2.12.1-216.1-d Hilbert modular form 2.2.12.1-216.1-b Hilbert modular form 2.2.12.1-216.1-d $1$ $1$ $1 - 3 T^{2} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-31104-1.1-c1e2-0-1 Elliptic curve 2.2.12.1-216.1-a Elliptic curve 2.2.12.1-216.1-c Hilbert modular form 2.2.12.1-216.1-a Hilbert modular form 2.2.12.1-216.1-c $1$ $1$ $1 - 3 T^{2} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-31147-1.1-c1e2-0-0 Genus 2 curve 31147.a $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + 4 T^{2} + 9 T^{4}$ $1 + 2 T + 4 T^{2} + 10 T^{3} + 25 T^{4}$ $1 - 4 T^{2} + 49 T^{4}$
4-31375-1.1-c1e2-0-3 Elliptic curve 2.2.5.1-1255.1-a Elliptic curve 2.2.5.1-1255.2-a Hilbert modular form 2.2.5.1-1255.1-a Hilbert modular form 2.2.5.1-1255.2-a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 4 T^{2} + 9 T^{4}$ $1 + T$ $1 - 4 T^{2} + 49 T^{4}$
4-32275-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-1291.1-b Elliptic curve 2.2.5.1-1291.2-b Hilbert modular form 2.2.5.1-1291.1-b Hilbert modular form 2.2.5.1-1291.2-b $1 + T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
4-33100-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-1324.1-b Elliptic curve 2.2.5.1-1324.2-b Hilbert modular form 2.2.5.1-1324.1-b Hilbert modular form 2.2.5.1-1324.2-b $1 + T^{2}$ $1 + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $1 - 4 T^{2} + 49 T^{4}$
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