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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-39e2-1.1-c1e2-0-1 Elliptic curve 2.2.13.1-9.1-a Hilbert modular form 2.2.13.1-9.1-a Modular form 39.2.b.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )^{2}$ $( 1 - 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-1947-1.1-c1e2-0-0 Genus 2 curve 1947.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )( 1 - T + 3 T^{2} )$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - T - 2 T^{2} - 7 T^{3} + 49 T^{4}$
4-1975-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-79.1-a Elliptic curve 2.2.5.1-79.2-a Hilbert modular form 2.2.5.1-79.1-a Hilbert modular form 2.2.5.1-79.2-a $1 - T^{2} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 2 T + 5 T^{2}$ $1 + 2 T^{2} + 49 T^{4}$
4-1995-1.1-c1e2-0-0 Genus 2 curve 1995.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )( 1 + 3 T^{2} )$ $( 1 + T )( 1 - 2 T + 5 T^{2} )$ $( 1 + T )( 1 + 2 T + 7 T^{2} )$
4-2169-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-241.1-a Bianchi modular form 2.0.3.1-241.2-a Elliptic curve 2.0.3.1-241.1-a Elliptic curve 2.0.3.1-241.2-a Genus 2 curve 2169.a $1 - T^{2} + 4 T^{4}$ $1 + 3 T^{2}$ $( 1 - 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2457-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-273.1-a Bianchi modular form 2.0.3.1-273.4-a Elliptic curve 2.0.3.1-273.1-a Elliptic curve 2.0.3.1-273.4-a Genus 2 curve 2457.b $1 - T^{2} + 4 T^{4}$ $1 + T$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 + T )( 1 + 7 T^{2} )$
4-2475-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-99.1-a Elliptic curve 2.2.5.1-99.2-a Hilbert modular form 2.2.5.1-99.1-a Hilbert modular form 2.2.5.1-99.2-a $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 + T )$ $1 + 2 T + 5 T^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2745-1.1-c1e2-0-0 Genus 2 curve 2745.a $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 + T )$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-3087-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-343.2-a Bianchi modular form 2.0.3.1-343.3-a Elliptic curve 2.0.3.1-343.2-a Elliptic curve 2.0.3.1-343.3-a $1 - T^{2} + 4 T^{4}$ $1 + 3 T^{2}$ $1 - 2 T^{2} + 25 T^{4}$ $1 + T$
4-3165-1.1-c1e2-0-0 Genus 2 curve 3165.a $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 + T + 3 T^{2} )$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $1 - T + 6 T^{2} - 7 T^{3} + 49 T^{4}$
4-3239-1.1-c1e2-0-1 Genus 2 curve 3239.b $1 - T^{2} + 4 T^{4}$ $1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $( 1 - T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-3267-1.1-c1e2-0-1 Bianchi modular form 2.0.11.1-27.2-a Bianchi modular form 2.0.11.1-27.3-a Elliptic curve 2.0.11.1-27.2-a Elliptic curve 2.0.11.1-27.3-a $1 - T^{2} + 4 T^{4}$ $1 + T$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 6 T^{2} + 49 T^{4}$
4-3417-1.1-c1e2-0-0 Genus 2 curve 3417.a $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-3431-1.1-c1e2-0-0 Genus 2 curve 3431.a $1 - T^{2} + 4 T^{4}$ $1 - T + 2 T^{2} - 3 T^{3} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-3591-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-399.2-a Bianchi modular form 2.0.3.1-399.3-a Elliptic curve 2.0.3.1-399.2-a Elliptic curve 2.0.3.1-399.3-a $1 - T^{2} + 4 T^{4}$ $1 + T$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + 7 T^{2} )$
4-3591-1.1-c1e2-0-1 Genus 2 curve 3591.a $1 - T^{2} + 4 T^{4}$ $1 - T$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 + T )( 1 + 7 T^{2} )$
4-3625-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-145.1-b Elliptic curve 2.2.5.1-145.2-b Hilbert modular form 2.2.5.1-145.1-b Hilbert modular form 2.2.5.1-145.2-b $1 - T^{2} + 4 T^{4}$ $( 1 + 3 T^{2} )^{2}$ $1 - T$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-3875-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-155.1-a Elliptic curve 2.2.5.1-155.2-a Hilbert modular form 2.2.5.1-155.1-a Hilbert modular form 2.2.5.1-155.2-a $1 - T^{2} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + T$ $1 + 6 T^{2} + 49 T^{4}$
4-63e2-1.1-c1e2-0-2 Genus 2 curve 3969.c Modular form 63.2.i.a $1 - T^{2} + 4 T^{4}$ $1 + 3 T^{2}$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - 4 T + 7 T^{2}$
4-4275-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-475.1-a Bianchi modular form 2.0.3.1-475.2-a Elliptic curve 2.0.3.1-475.1-a Elliptic curve 2.0.3.1-475.2-a $1 - T^{2} + 4 T^{4}$ $1 + 3 T^{2}$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-4331-1.1-c1e2-0-0 Genus 2 curve 4331.a $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $1 + T + 6 T^{2} + 7 T^{3} + 49 T^{4}$
4-4431-1.1-c1e2-0-0 Genus 2 curve 4431.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )( 1 - 2 T + 3 T^{2} )$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $( 1 - T )( 1 + 7 T^{2} )$
4-4475-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-179.1-a Elliptic curve 2.2.5.1-179.2-a Hilbert modular form 2.2.5.1-179.1-a Hilbert modular form 2.2.5.1-179.2-a $1 - T^{2} + 4 T^{4}$ $1 + 9 T^{4}$ $1 + 5 T^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-4667-1.1-c1e2-0-0 Genus 2 curve 4667.a $1 - T^{2} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )( 1 + 3 T^{2} )$ $1 + T + 5 T^{3} + 25 T^{4}$ $( 1 + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-4725-1.1-c1e2-0-0 Genus 2 curve 4725.a $1 - T^{2} + 4 T^{4}$ $1 + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $( 1 - T )( 1 - 2 T + 7 T^{2} )$
4-69e2-1.1-c1e2-0-0 Modular form 69.2.a.b $1 - T^{2} + 4 T^{4}$ $( 1 + T )^{2}$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4}$
4-4863-1.1-c1e2-0-0 Genus 2 curve 4863.a $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 + 2 T + 3 T^{2} )$ $1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4}$ $1 - 10 T^{2} + 49 T^{4}$
4-5125-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-205.1-b Elliptic curve 2.2.5.1-205.2-b Hilbert modular form 2.2.5.1-205.1-b Hilbert modular form 2.2.5.1-205.2-b $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - T$ $1 - 10 T^{2} + 49 T^{4}$
4-5211-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-579.1-b Bianchi modular form 2.0.3.1-579.2-b Elliptic curve 2.0.3.1-579.1-b Elliptic curve 2.0.3.1-579.2-b $1 - T^{2} + 4 T^{4}$ $1 + T$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-5225-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-209.1-c Elliptic curve 2.2.5.1-209.4-c Hilbert modular form 2.2.5.1-209.1-c Hilbert modular form 2.2.5.1-209.4-c $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 + 6 T^{2} + 49 T^{4}$
4-5225-1.1-c1e2-0-4 Elliptic curve 2.2.5.1-209.2-a Elliptic curve 2.2.5.1-209.3-a Hilbert modular form 2.2.5.1-209.2-a Hilbert modular form 2.2.5.1-209.3-a $1 - T^{2} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 - 2 T + 5 T^{2}$ $1 - 6 T^{2} + 49 T^{4}$
4-5427-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-603.1-a Bianchi modular form 2.0.3.1-603.2-a Elliptic curve 2.0.3.1-603.1-a Elliptic curve 2.0.3.1-603.2-a $1 - T^{2} + 4 T^{4}$ $1$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 + 7 T^{2} )^{2}$
4-5497-1.1-c1e2-0-2 Genus 2 curve 5497.d $1 - T^{2} + 4 T^{4}$ $1 - T + 2 T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - T + 6 T^{2} - 7 T^{3} + 49 T^{4}$
4-5591-1.1-c1e2-0-0 Genus 2 curve 5591.a $1 - T^{2} + 4 T^{4}$ $1 - T + 2 T^{2} - 3 T^{3} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $1 + T + 6 T^{2} + 7 T^{3} + 49 T^{4}$
4-5637-1.1-c1e2-0-0 Genus 2 curve 5637.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )( 1 - 2 T + 3 T^{2} )$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - 3 T + 6 T^{2} - 21 T^{3} + 49 T^{4}$
4-5655-1.1-c1e2-0-0 Genus 2 curve 5655.b $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 + 3 T^{2} )$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-5775-1.1-c1e2-0-0 Genus 2 curve 5775.a $1 - T^{2} + 4 T^{4}$ $( 1 - T )( 1 + 3 T^{2} )$ $( 1 - T )( 1 + T )$ $( 1 - T )( 1 + 7 T^{2} )$
4-5859-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-651.2-a Bianchi modular form 2.0.3.1-651.3-a Elliptic curve 2.0.3.1-651.2-a Elliptic curve 2.0.3.1-651.3-a $1 - T^{2} + 4 T^{4}$ $1 - T$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 7 T^{2} )$
4-77e2-1.1-c1e2-0-2 Genus 2 curve 5929.b Modular form 77.2.a.d $1 - T^{2} + 4 T^{4}$ $1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$ $( 1 + 2 T + 5 T^{2} )^{2}$ $( 1 - T )^{2}$
4-5975-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-239.1-a Elliptic curve 2.2.5.1-239.2-a Hilbert modular form 2.2.5.1-239.1-a Hilbert modular form 2.2.5.1-239.2-a $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 6 T^{2} + 49 T^{4}$
4-5975-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-239.1-b Elliptic curve 2.2.5.1-239.2-b Hilbert modular form 2.2.5.1-239.1-b Hilbert modular form 2.2.5.1-239.2-b $1 - T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 - T + 5 T^{2}$ $1 + 6 T^{2} + 49 T^{4}$
4-6105-1.1-c1e2-0-0 Genus 2 curve 6105.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )( 1 - 2 T + 3 T^{2} )$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-6111-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-679.1-a Bianchi modular form 2.0.3.1-679.4-a Elliptic curve 2.0.3.1-679.1-a Elliptic curve 2.0.3.1-679.4-a $1 - T^{2} + 4 T^{4}$ $1 + 3 T^{2}$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 + T )( 1 - 4 T + 7 T^{2} )$
4-6265-1.1-c1e2-0-0 Genus 2 curve 6265.a $1 - T^{2} + 4 T^{4}$ $1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $( 1 + T )( 1 - 4 T + 7 T^{2} )$
4-6267-1.1-c1e2-0-0 Genus 2 curve 6267.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )( 1 - T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4}$
4-6273-1.1-c1e2-0-0 Genus 2 curve 6273.a $1 - T^{2} + 4 T^{4}$ $1 + T^{2}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 4 T + 10 T^{2} - 28 T^{3} + 49 T^{4}$
4-6307-1.1-c1e2-0-0 Genus 2 curve 6307.a $1 - T^{2} + 4 T^{4}$ $1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 2 T + 7 T^{2} )$
4-6343-1.1-c1e2-0-0 Genus 2 curve 6343.a $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-6429-1.1-c1e2-0-0 Genus 2 curve 6429.a $1 - T^{2} + 4 T^{4}$ $( 1 + T )( 1 - 3 T + 3 T^{2} )$ $( 1 + 2 T + 5 T^{2} )^{2}$ $1 - 3 T + 6 T^{2} - 21 T^{3} + 49 T^{4}$
4-6571-1.1-c1e2-0-0 Genus 2 curve 6571.a $1 - T^{2} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )( 1 + 3 T^{2} )$ $( 1 + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 7 T^{2} )$
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