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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-644-1.1-c1e2-0-1 Genus 2 curve 644.b $1 + T^{2}$ $1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 2 T + 7 T^{2} )$
4-731-1.1-c1e2-0-0 Genus 2 curve 731.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 2 T + 4 T^{2} + 14 T^{3} + 49 T^{4}$
4-1468-1.1-c1e2-0-0 Genus 2 curve 1468.b $( 1 - T )( 1 + T )$ $1 + T + T^{2} + 3 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 4 T + 8 T^{2} + 28 T^{3} + 49 T^{4}$
4-1539-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-171.1-a Bianchi modular form 2.0.3.1-171.2-a Elliptic curve 2.0.3.1-171.1-a Elliptic curve 2.0.3.1-171.2-a $1 + T^{2} + 4 T^{4}$ $1$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2106-1.1-c1e2-0-0 Genus 2 curve 2106.a $( 1 - T )( 1 + 2 T^{2} )$ $1 + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2176-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-34.1-a Elliptic curve 2.2.8.1-34.2-a Hilbert modular form 2.2.8.1-34.1-a Hilbert modular form 2.2.8.1-34.2-a $1 + T$ $1 - 4 T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2348-1.1-c1e2-0-1 Genus 2 curve 2348.a $1 + T^{2}$ $1 + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-2547-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-283.1-a Bianchi modular form 2.0.3.1-283.2-a Elliptic curve 2.0.3.1-283.1-a Elliptic curve 2.0.3.1-283.2-a $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + 3 T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-2613-1.1-c1e2-0-0 Genus 2 curve 2613.a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $1 + T - 3 T^{2} + 7 T^{3} + 49 T^{4}$
4-2743-1.1-c1e2-0-0 Genus 2 curve 2743.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T + T^{2} + 3 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2758-1.1-c1e2-0-0 Genus 2 curve 2758.a $( 1 + T )( 1 + 2 T^{2} )$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 5 T + 7 T^{2} )$
4-2873-1.1-c1e2-0-0 Elliptic curve 2.2.13.1-17.1-a Elliptic curve 2.2.13.1-17.2-a Hilbert modular form 2.2.13.1-17.1-a Hilbert modular form 2.2.13.1-17.2-a $1 - 2 T^{2} + 4 T^{4}$ $( 1 - T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 4 T^{2} + 49 T^{4}$
4-3168-1.1-c1e2-0-0 Elliptic curve 2.2.12.1-22.1-a Elliptic curve 2.2.12.1-22.2-a Hilbert modular form 2.2.12.1-22.1-a Hilbert modular form 2.2.12.1-22.2-a $1 + T$ $1 - T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $1 - 5 T^{2} + 49 T^{4}$
4-3168-1.1-c1e2-0-1 Elliptic curve 2.2.12.1-22.1-b Elliptic curve 2.2.12.1-22.2-b Hilbert modular form 2.2.12.1-22.1-b Hilbert modular form 2.2.12.1-22.2-b $1 - T$ $1 + T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $1 - 5 T^{2} + 49 T^{4}$
4-3349-1.1-c1e2-0-1 Genus 2 curve 3349.b $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 3 T + 6 T^{2} + 21 T^{3} + 49 T^{4}$
4-3779-1.1-c1e2-0-0 Genus 2 curve 3779.b $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $1 + 2 T + 5 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $1 - 2 T + 3 T^{2} - 14 T^{3} + 49 T^{4}$
4-3846-1.1-c1e2-0-0 Genus 2 curve 3846.a $( 1 + T )( 1 + 2 T^{2} )$ $( 1 + T )( 1 + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 6 T + 18 T^{2} + 42 T^{3} + 49 T^{4}$
4-4293-1.1-c1e2-0-0 Genus 2 curve 4293.c $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1$ $1 + 4 T^{2} + 25 T^{4}$ $1 - T + 3 T^{2} - 7 T^{3} + 49 T^{4}$
4-4293-1.1-c1e2-0-1 Genus 2 curve 4293.a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T^{2} )$ $1$ $1 + 4 T^{2} + 25 T^{4}$ $1 - T + 3 T^{2} - 7 T^{3} + 49 T^{4}$
4-4324-1.1-c1e2-0-0 Genus 2 curve 4324.a $( 1 - T )( 1 + T )$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-4418-1.1-c1e2-0-0 Genus 2 curve 4418.a $( 1 - T )( 1 + 2 T^{2} )$ $( 1 - 3 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $1 + T + 5 T^{2} + 7 T^{3} + 49 T^{4}$
4-4671-1.1-c1e2-0-0 Genus 2 curve 4671.a $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + T$ $1 + 4 T^{2} + 25 T^{4}$ $1 + T - 4 T^{2} + 7 T^{3} + 49 T^{4}$
4-4707-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-523.1-a Bianchi modular form 2.0.3.1-523.2-a Elliptic curve 2.0.3.1-523.1-a Elliptic curve 2.0.3.1-523.2-a $1 + T^{2} + 4 T^{4}$ $1 - T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-4788-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-532.2-a Bianchi modular form 2.0.3.1-532.3-a Elliptic curve 2.0.3.1-532.2-a Elliptic curve 2.0.3.1-532.3-a $1 + T^{2}$ $1 + T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 - 3 T + 7 T^{2} )$
4-4824-1.1-c1e2-0-0 Genus 2 curve 4824.a $1 - T$ $1 + T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 2 T + 4 T^{2} + 14 T^{3} + 49 T^{4}$
4-4977-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-553.2-a Bianchi modular form 2.0.3.1-553.3-a Elliptic curve 2.0.3.1-553.2-a Elliptic curve 2.0.3.1-553.3-a $1 + 2 T^{2} + 4 T^{4}$ $1 + 2 T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 3 T + 7 T^{2} )$
4-5173-1.1-c1e2-0-0 Genus 2 curve 5173.a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 - T - T^{2} - 3 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + 2 T + 7 T^{2} )$
4-5572-1.1-c1e2-0-1 Genus 2 curve 5572.a $1 + T + T^{2}$ $( 1 - T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + 4 T + 7 T^{2} )$
4-5769-1.1-c1e2-0-1 Genus 2 curve 5769.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 2 T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 2 T^{2} + 49 T^{4}$
4-5867-1.1-c1e2-0-0 Genus 2 curve 5867.a $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 3 T + 5 T^{2} + 9 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $1 - 3 T + 12 T^{2} - 21 T^{3} + 49 T^{4}$
4-5964-1.1-c1e2-0-0 Genus 2 curve 5964.a $1 + T + T^{2}$ $( 1 - T )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 4 T + 7 T^{2} )$
4-6016-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-94.1-a Elliptic curve 2.2.8.1-94.2-a Hilbert modular form 2.2.8.1-94.1-a Hilbert modular form 2.2.8.1-94.2-a $1 + T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )^{2}$
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 $1 + T + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-6813-1.1-c1e2-0-2 Bianchi modular form 2.0.3.1-757.1-a Bianchi modular form 2.0.3.1-757.2-a Elliptic curve 2.0.3.1-757.1-a Elliptic curve 2.0.3.1-757.2-a $1 + T^{2} + 4 T^{4}$ $1 - T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )^{2}$
4-6826-1.1-c1e2-0-0 Genus 2 curve 6826.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 - 2 T + 4 T^{2} - 6 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-6831-1.1-c1e2-0-0 Genus 2 curve 6831.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 8 T^{2} + 49 T^{4}$
4-6964-1.1-c1e2-0-0 Genus 2 curve 6964.b $( 1 - T )( 1 + T )$ $1 + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $1 - 10 T^{2} + 49 T^{4}$
4-7013-1.1-c1e2-0-0 Genus 2 curve 7013.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 7 T^{2} )$
4-7332-1.1-c1e2-0-0 Genus 2 curve 7332.a $( 1 - T )( 1 + T )$ $( 1 - T )( 1 + T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-7359-1.1-c1e2-0-1 Genus 2 curve 7359.a $1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4}$ $( 1 + T )( 1 - T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 4 T^{2} + 49 T^{4}$
4-7594-1.1-c1e2-0-0 Genus 2 curve 7594.b $( 1 + T )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-7616-1.1-c1e2-0-2 Genus 2 curve 7616.a $1 - T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T )( 1 - 2 T + 7 T^{2} )$
4-7616-1.1-c1e2-0-3 Elliptic curve 2.2.8.1-119.1-c Elliptic curve 2.2.8.1-119.4-c Hilbert modular form 2.2.8.1-119.1-c Hilbert modular form 2.2.8.1-119.4-c $1 + 2 T + 2 T^{2}$ $1 + 4 T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 4 T + 7 T^{2} )$
4-7616-1.1-c1e2-0-4 Elliptic curve 2.2.8.1-119.1-a Elliptic curve 2.2.8.1-119.4-a Hilbert modular form 2.2.8.1-119.1-a Hilbert modular form 2.2.8.1-119.4-a $1 - 2 T + 2 T^{2}$ $1 + 4 T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + 7 T^{2} )$
4-7877-1.1-c1e2-0-1 Genus 2 curve 7877.b $1 + T + 2 T^{3} + 4 T^{4}$ $( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-7927-1.1-c1e2-0-0 Genus 2 curve 7927.a $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-8064-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-126.1-a Elliptic curve 2.2.8.1-126.2-a Hilbert modular form 2.2.8.1-126.1-a Hilbert modular form 2.2.8.1-126.2-a $1 + T$ $( 1 - T )( 1 + T )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 - 2 T + 7 T^{2} )$
4-8064-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-126.1-c Elliptic curve 2.2.8.1-126.2-c Hilbert modular form 2.2.8.1-126.1-c Hilbert modular form 2.2.8.1-126.2-c $1 - T$ $1 + T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + 2 T + 7 T^{2} )$
4-8064-1.1-c1e2-0-2 Genus 2 curve 8064.b $1 - T$ $1 + T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + 2 T + 7 T^{2} )$
4-8619-1.1-c1e2-0-0 Elliptic curve 2.2.13.1-51.1-c Elliptic curve 2.2.13.1-51.4-c Hilbert modular form 2.2.13.1-51.1-c Hilbert modular form 2.2.13.1-51.4-c $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $( 1 + T )( 1 + 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 4 T^{2} + 49 T^{4}$
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