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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-7803-1.1-c1e2-0-0 Genus 2 curve 7803.b $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-10693-1.1-c1e2-0-0 Genus 2 curve 10693.a $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$ $( 1 + 2 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-13527-1.1-c1e2-0-1 Genus 2 curve 13527.d $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 3 T^{2}$ $1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-15126-1.1-c1e2-0-0 Genus 2 curve 15126.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + 3 T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-19090-1.1-c1e2-0-0 Genus 2 curve 19090.a $( 1 - T )( 1 + T + 2 T^{2} )$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$ $( 1 - T )( 1 + 4 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-27456-1.1-c1e2-0-0 Genus 2 curve 27456.a $1 + T + 2 T^{2}$ $( 1 + T )( 1 - 2 T + 3 T^{2} )$ $1 - T - 5 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-33233-1.1-c1e2-0-0 Genus 2 curve 33233.a $1 - T^{2} + 4 T^{4}$ $1 - T + T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-35629-1.1-c1e2-0-0 Genus 2 curve 35629.a $1 - T^{2} + 4 T^{4}$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$ $1 + T + 5 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-38988-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-4332.1-a Bianchi modular form 2.0.3.1-4332.3-a Elliptic curve 2.0.3.1-4332.1-a Elliptic curve 2.0.3.1-4332.3-a $1 + T^{2}$ $1 - T$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-42250-1.1-c1e2-0-1 Elliptic curve 2.2.65.1-10.1-a Elliptic curve 2.2.65.1-10.2-a Hilbert modular form 2.2.65.1-10.1-a Hilbert modular form 2.2.65.1-10.2-a $( 1 - T )( 1 + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - T$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-45177-1.1-c1e2-0-3 Elliptic curve 2.2.37.1-33.2-b Elliptic curve 2.2.37.1-33.3-b Hilbert modular form 2.2.37.1-33.2-b Hilbert modular form 2.2.37.1-33.3-b $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 - T + 3 T^{2} )$ $1 + 2 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-6e6-1.1-c1e2-0-3 Elliptic curve 2.2.8.1-729.1-i Elliptic curve 2.2.8.1-729.1-k Hilbert modular form 2.2.8.1-729.1-i Hilbert modular form 2.2.8.1-729.1-k $1 + 2 T + 2 T^{2}$ $1$ $1 + 3 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-6e6-1.1-c1e2-0-9 Elliptic curve 2.2.8.1-729.1-e Elliptic curve 2.2.8.1-729.1-h Hilbert modular form 2.2.8.1-729.1-e Hilbert modular form 2.2.8.1-729.1-h $1 - 2 T + 2 T^{2}$ $1$ $1 + 3 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-47360-1.1-c1e2-0-8 Genus 2 curve 47360.a $1$ $( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $( 1 - T )( 1 + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-222e2-1.1-c1e2-0-3 Elliptic curve 2.2.37.1-36.2-d Elliptic curve 2.2.37.1-36.3-d Hilbert modular form 2.2.37.1-36.2-d Hilbert modular form 2.2.37.1-36.3-d $1 + T^{2}$ $1 - T + 3 T^{2}$ $1 + 2 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-50714-1.1-c1e2-0-0 Genus 2 curve 50714.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $1 - T - 5 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-51462-1.1-c1e2-0-0 Genus 2 curve 51462.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + T$ $( 1 - 2 T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-51543-1.1-c1e2-0-0 Genus 2 curve 51543.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T + 3 T^{2}$ $( 1 - 3 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-53295-1.1-c1e2-0-0 Genus 2 curve 53295.a $1 - T - 2 T^{3} + 4 T^{4}$ $( 1 + T )( 1 + 3 T^{2} )$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-55626-1.1-c1e2-0-1 Genus 2 curve 55626.a $( 1 - T )( 1 + T + 2 T^{2} )$ $( 1 - T )( 1 + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-55981-1.1-c1e2-0-0 Genus 2 curve 55981.a $1 - T - 2 T^{3} + 4 T^{4}$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-56061-1.1-c1e2-0-0 Genus 2 curve 56061.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + T )$ $1 + T + 3 T^{2} + 5 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-61178-1.1-c1e2-0-0 Genus 2 curve 61178.b $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4}$ $1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-67485-1.1-c1e2-0-0 Genus 2 curve 67485.a $1 + T^{2} + 4 T^{4}$ $( 1 + T )( 1 + T + 3 T^{2} )$ $( 1 + T )( 1 - 3 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-74430-1.1-c1e2-0-0 Genus 2 curve 74430.a $( 1 + T )( 1 - T + 2 T^{2} )$ $1 + T^{2}$ $( 1 + T )( 1 + 3 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-76352-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-1193.1-b Elliptic curve 2.2.8.1-1193.2-b Hilbert modular form 2.2.8.1-1193.1-b Hilbert modular form 2.2.8.1-1193.2-b $1 - T + 2 T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-77372-1.1-c1e2-0-0 Elliptic curve 2.2.29.1-92.1-a Elliptic curve 2.2.29.1-92.2-a Hilbert modular form 2.2.29.1-92.1-a Hilbert modular form 2.2.29.1-92.2-a $1 + T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-85077-1.1-c1e2-0-0 Genus 2 curve 85077.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 3 T^{2}$ $1 + T + 5 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-85360-1.1-c1e2-0-0 Genus 2 curve 85360.a $1 + 2 T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + T )( 1 + T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-89944-1.1-c1e2-0-0 Genus 2 curve 89944.a $1 + T + 2 T^{2}$ $1 - T + 3 T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-105472-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-1648.1-c Elliptic curve 2.2.8.1-1648.2-c Hilbert modular form 2.2.8.1-1648.1-c Hilbert modular form 2.2.8.1-1648.2-c $1$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 8 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-327e2-1.1-c1e2-0-0 Elliptic curve 2.2.109.1-9.2-b Elliptic curve 2.2.109.1-9.3-b Hilbert modular form 2.2.109.1-9.2-b Hilbert modular form 2.2.109.1-9.3-b $1 - T^{2} + 4 T^{4}$ $1 + 3 T + 3 T^{2}$ $( 1 - 2 T + 5 T^{2} )( 1 - T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-327e2-1.1-c1e2-0-5 Elliptic curve 2.2.109.1-9.2-a Elliptic curve 2.2.109.1-9.3-a Hilbert modular form 2.2.109.1-9.2-a Hilbert modular form 2.2.109.1-9.3-a $1 + T^{2} + 4 T^{4}$ $1 - 3 T + 3 T^{2}$ $( 1 - 2 T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-111911-1.1-c1e2-0-0 Genus 2 curve 111911.a $1 - T^{2} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 2 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-113600-1.1-c1e2-0-6 Genus 2 curve 113600.b $1 + T$ $( 1 - 3 T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 4 T + 5 T^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-342e2-1.1-c1e2-0-10 Modular form 342.2.j.b $1 - T + T^{2}$ $1 + 3 T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-342e2-1.1-c1e2-0-25 Modular form 342.2.n.c $( 1 - T )^{2}$ $1 + 3 T^{2}$ $1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-120704-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-1886.1-a Elliptic curve 2.2.8.1-1886.4-a Hilbert modular form 2.2.8.1-1886.1-a Hilbert modular form 2.2.8.1-1886.4-a $1 - T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-120832-1.1-c1e2-0-4 Genus 2 curve 120832.c $1$ $( 1 - T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-126684-1.1-c1e2-0-0 Genus 2 curve 126684.a $( 1 - T )( 1 + T )$ $1$ $1 - 2 T + 8 T^{2} - 10 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-130299-1.1-c1e2-0-4 Genus 2 curve 130299.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T )( 1 - T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-135375-1.1-c1e2-0-0 Genus 2 curve 135375.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $( 1 + T )( 1 - T + 3 T^{2} )$ $1 + T$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-137776-1.1-c1e2-0-0 Genus 2 curve 137776.a $1 + T + 2 T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 5 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-138269-1.1-c1e2-0-1 Elliptic curve 2.2.37.1-101.1-a Elliptic curve 2.2.37.1-101.2-a Hilbert modular form 2.2.37.1-101.1-a Hilbert modular form 2.2.37.1-101.2-a $1 + T^{2} + 4 T^{4}$ $( 1 - 3 T + 3 T^{2} )( 1 - 2 T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-143065-1.1-c1e2-0-0 Genus 2 curve 143065.a $1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - T )( 1 - 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-147852-1.1-c1e2-0-4 Elliptic curve 2.2.37.1-108.3-c Elliptic curve 2.2.37.1-108.4-c Hilbert modular form 2.2.37.1-108.3-c Hilbert modular form 2.2.37.1-108.4-c $1 + T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 2 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-148528-1.1-c1e2-0-0 Genus 2 curve 148528.a $1 - T + 2 T^{2}$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$ $1 + 2 T + 9 T^{2} + 10 T^{3} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-390e2-1.1-c1e2-0-7 Modular form 390.2.i.d $1 - T + T^{2}$ $1 + T + T^{2}$ $( 1 + T )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-152354-1.1-c1e2-0-0 Genus 2 curve 152354.a $( 1 + T )( 1 - T + 2 T^{2} )$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-158272-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-2473.1-a Elliptic curve 2.2.8.1-2473.2-a Hilbert modular form 2.2.8.1-2473.1-a Hilbert modular form 2.2.8.1-2473.2-a $1 - 2 T + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $1 - 4 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
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