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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-22e2-1.1-c1e2-0-0 Genus 2 curve 484.a $1 + 2 T + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-847-1.1-c1e2-0-0 Genus 2 curve 847.d $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )( 1 - T + 5 T^{2} )$ $( 1 - T )( 1 + 2 T + 7 T^{2} )$
4-38e2-1.1-c1e2-0-1 Genus 2 curve 1444.a $( 1 - T )( 1 + T )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 3 T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-1900-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-76.1-a Elliptic curve 2.2.5.1-76.2-a Hilbert modular form 2.2.5.1-76.1-a Hilbert modular form 2.2.5.1-76.2-a $1 + T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - T + 5 T^{2}$ $1 + 49 T^{4}$
4-44e2-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-121.1-a Elliptic curve 2.0.4.1-121.1-a $1 + 2 T + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-2299-1.1-c1e2-0-1 Genus 2 curve 2299.b $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 + 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-50e2-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-100.1-b Genus 2 curve 2500.a Hilbert modular form 2.2.5.1-100.1-b $( 1 - T )( 1 + T )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-2944-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-46.1-a Elliptic curve 2.2.8.1-46.2-a Hilbert modular form 2.2.8.1-46.1-a Hilbert modular form 2.2.8.1-46.2-a $1 + T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-55e2-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-121.1-a Hilbert modular form 2.2.5.1-121.1-a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - T + 5 T^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-3601-1.1-c1e2-0-0 Genus 2 curve 3601.a $1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4}$
4-4961-1.1-c1e2-0-0 Genus 2 curve 4961.a $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-5248-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-82.1-a Elliptic curve 2.2.8.1-82.2-a Hilbert modular form 2.2.8.1-82.1-a Hilbert modular form 2.2.8.1-82.2-a $1 - T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 3 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-5324-1.1-c1e2-0-0 Genus 2 curve 5324.a $1 + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 3 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 7 T^{2} )$
4-5345-1.1-c1e2-0-0 Genus 2 curve 5345.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T )( 1 + 3 T + 5 T^{2} )$ $1 - T + 5 T^{2} - 7 T^{3} + 49 T^{4}$
4-5408-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-338.2-a Elliptic curve 2.0.4.1-338.2-a $1 + T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 3 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-74e2-1.1-c1e2-0-4 Genus 2 curve 5476.a $1 + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 + T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-76e2-1.1-c1e2-0-2 Genus 2 curve 5776.d $1 - T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 3 T + 7 T^{2} )^{2}$
4-77e2-1.1-c1e2-0-1 Bianchi modular form 2.0.7.1-121.2-a Elliptic curve 2.0.7.1-121.2-a $( 1 + 2 T + 2 T^{2} )^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $1 + 2 T + 7 T^{2}$
4-5975-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-239.1-c Elliptic curve 2.2.5.1-239.2-c Hilbert modular form 2.2.5.1-239.1-c Hilbert modular form 2.2.5.1-239.2-c $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 3 T + 5 T^{2}$ $1 - 6 T^{2} + 49 T^{4}$
4-6125-1.1-c1e2-0-0 Genus 2 curve 6125.a $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + T$ $( 1 - T )^{2}$
4-6125-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-245.1-a Hilbert modular form 2.2.5.1-245.1-a $( 1 + 2 T^{2} )^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + T$ $( 1 - T )( 1 + T )$
4-6784-1.1-c1e2-0-2 Genus 2 curve 6784.b $1 + T + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 + T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-7072-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-442.1-a Bianchi modular form 2.0.4.1-442.4-a Elliptic curve 2.0.4.1-442.1-a Elliptic curve 2.0.4.1-442.4-a $1 + T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )( 1 + 5 T^{2} )$ $( 1 - 7 T^{2} )^{2}$
4-7436-1.1-c1e2-0-0 Genus 2 curve 7436.c $( 1 + T )^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-7436-1.1-c1e2-0-2 Genus 2 curve 7436.a $( 1 - T )( 1 + T )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 3 T + 5 T^{2} )^{2}$ $( 1 + T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-88e2-1.1-c1e2-0-3 Elliptic curve 2.2.8.1-121.1-a Hilbert modular form 2.2.8.1-121.1-a $1 + 2 T + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $( 1 + 2 T + 7 T^{2} )^{2}$
4-88e2-1.1-c1e2-0-5 Bianchi modular form 2.0.4.1-484.1-a Elliptic curve 2.0.4.1-484.1-a $1$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 3 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-7900-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-316.1-a Elliptic curve 2.2.5.1-316.2-a Hilbert modular form 2.2.5.1-316.1-a Hilbert modular form 2.2.5.1-316.2-a $( 1 - T )( 1 + T )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 3 T + 5 T^{2}$ $( 1 - 7 T^{2} )^{2}$
4-8080-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-505.2-a Bianchi modular form 2.0.4.1-505.3-a Elliptic curve 2.0.4.1-505.2-a Elliptic curve 2.0.4.1-505.3-a $1 + T + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + T )( 1 + T + 5 T^{2} )$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-8492-1.1-c1e2-0-0 Genus 2 curve 8492.a $1 + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + T^{2} + 49 T^{4}$
4-8575-1.1-c1e2-0-2 Bianchi modular form 2.0.7.1-175.1-a Elliptic curve 2.0.7.1-175.1-a $( 1 + 2 T^{2} )^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T )( 1 + T )$ $1 - T$
4-8657-1.1-c1e2-0-0 Genus 2 curve 8657.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 2 T + 4 T^{2} + 10 T^{3} + 25 T^{4}$ $1 - 5 T^{2} + 49 T^{4}$
4-8726-1.1-c1e2-0-1 Genus 2 curve 8726.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 2 T + 10 T^{3} + 25 T^{4}$ $1 + 4 T + 13 T^{2} + 28 T^{3} + 49 T^{4}$
4-8753-1.1-c1e2-0-0 Genus 2 curve 8753.a $1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 2 T + 5 T^{2} - 10 T^{3} + 25 T^{4}$ $1 + 2 T + 14 T^{3} + 49 T^{4}$
4-8788-1.1-c1e2-0-3 Genus 2 curve 8788.a $( 1 - T )( 1 + T )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 3 T + 5 T^{2} )^{2}$ $( 1 + T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-9800-1.1-c1e2-0-1 Genus 2 curve 9800.a $1 + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + T )^{2}$ $( 1 - T )( 1 + T )$
4-10775-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-431.1-a Elliptic curve 2.2.5.1-431.2-a Hilbert modular form 2.2.5.1-431.1-a Hilbert modular form 2.2.5.1-431.2-a $1 - 2 T^{2} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-104e2-1.1-c1e2-0-14 Genus 2 curve 10816.d $1 + T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 + T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-10952-1.1-c1e2-0-1 Genus 2 curve 10952.c $1 + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 5 T^{2} )^{2}$ $( 1 + T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-11230-1.1-c1e2-0-0 Genus 2 curve 11230.a $( 1 - T )( 1 + T + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T )( 1 + 3 T + 5 T^{2} )$ $( 1 - T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-11360-1.1-c1e2-0-0 Genus 2 curve 11360.a $1$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + T )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-11552-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-722.1-a Elliptic curve 2.0.4.1-722.1-a $1 + T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-11552-1.1-c1e2-0-3 Genus 2 curve 11552.b $1 + T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 5 T^{2} )^{2}$ $( 1 + T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-11552-1.1-c1e2-0-4 Bianchi modular form 2.0.4.1-722.1-b Elliptic curve 2.0.4.1-722.1-b $1 - T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + 4 T + 5 T^{2} )^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-11900-1.1-c1e2-0-0 Genus 2 curve 11900.a $1 + T + T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + T^{2}$ $( 1 - T )( 1 + 3 T + 7 T^{2} )$
4-12025-1.1-c1e2-0-1 Genus 2 curve 12025.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 2 T + 5 T^{2}$ $1 - 2 T - 14 T^{3} + 49 T^{4}$
4-110e2-1.1-c1e2-0-5 Elliptic curve 2.2.5.1-484.2-a Elliptic curve 2.2.5.1-484.3-a Hilbert modular form 2.2.5.1-484.2-a Hilbert modular form 2.2.5.1-484.3-a $( 1 - T )( 1 + T )$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 3 T + 5 T^{2}$ $1 + T^{2} + 49 T^{4}$
4-110e2-1.1-c1e2-0-7 Elliptic curve 2.2.5.1-484.2-b Elliptic curve 2.2.5.1-484.3-b Hilbert modular form 2.2.5.1-484.2-b Hilbert modular form 2.2.5.1-484.3-b $1 + T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 3 T + 5 T^{2}$ $1 - T^{2} + 49 T^{4}$
4-12347-1.1-c1e2-0-0 Genus 2 curve 12347.a $1 + T + 2 T^{3} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 + 2 T + 5 T^{2} + 10 T^{3} + 25 T^{4}$ $1 - 5 T^{2} + 49 T^{4}$
4-12593-1.1-c1e2-0-0 Genus 2 curve 12593.c $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - T )( 1 + T )$
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