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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-691-1.1-c1e2-0-0 Genus 2 curve 691.a $1 + T + 2 T^{3} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 + 2 T + 5 T^{2} )^{2}$ $1 + T + 6 T^{2} + 7 T^{3} + 49 T^{4}$
4-775-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-31.1-a Elliptic curve 2.2.5.1-31.2-a Hilbert modular form 2.2.5.1-31.1-a Hilbert modular form 2.2.5.1-31.2-a $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-1051-1.1-c1e2-0-0 Genus 2 curve 1051.b $1 + T + 2 T^{3} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-40e2-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-64.1-a Hilbert modular form 2.2.5.1-64.1-a Modular form 40.2.c.a $1$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 10 T^{2} + 49 T^{4}$
4-1952-1.1-c1e2-0-0 Genus 2 curve 1952.b $1$ $1 - 2 T^{2} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $1 + T + 6 T^{2} + 7 T^{3} + 49 T^{4}$
4-2117-1.1-c1e2-0-0 Genus 2 curve 2117.a $1 + T + 2 T^{3} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2254-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-46.2-a Bianchi modular form 2.0.7.1-46.3-a Elliptic curve 2.0.7.1-46.2-a Elliptic curve 2.0.7.1-46.3-a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $1 + 7 T^{2}$
4-2560-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-160.1-a Bianchi modular form 2.0.4.1-160.2-a Elliptic curve 2.0.4.1-160.1-a Elliptic curve 2.0.4.1-160.2-a Genus 2 curve 2560.a $1$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2600-1.1-c1e2-0-0 Genus 2 curve 2600.a $1 - T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-2837-1.1-c1e2-0-0 Genus 2 curve 2837.b $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + T - 2 T^{2} + 7 T^{3} + 49 T^{4}$
4-2912-1.1-c1e2-0-0 Genus 2 curve 2912.a $1$ $1 - 2 T^{2} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $( 1 - T )( 1 + 7 T^{2} )$
4-55e2-1.1-c1e2-0-1 Modular form 55.2.a.b $1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 + T )^{2}$ $( 1 + 2 T + 7 T^{2} )^{2}$
4-3280-1.1-c1e2-0-0 Genus 2 curve 3280.a $1 - T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 + T )( 1 - 2 T + 5 T^{2} )$ $1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-3397-1.1-c1e2-0-0 Genus 2 curve 3397.a $1 + T + 2 T^{3} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 7 T^{2} )$
4-3584-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-56.1-a Elliptic curve 2.2.8.1-56.2-a Genus 2 curve 3584.a Hilbert modular form 2.2.8.1-56.1-a Hilbert modular form 2.2.8.1-56.2-a $1$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 + T )( 1 + 7 T^{2} )$
4-3746-1.1-c1e2-0-0 Genus 2 curve 3746.b $( 1 - T )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 6 T^{2} + 49 T^{4}$
4-3970-1.1-c1e2-0-0 Genus 2 curve 3970.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 + T )( 1 - 2 T + 5 T^{2} )$ $( 1 + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-2e12-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-64.1-a Genus 2 curve 4096.b Hilbert modular form 2.2.8.1-64.1-a Modular form 64.2.b.a $1$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-4100-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-164.1-a Elliptic curve 2.2.5.1-164.2-a Hilbert modular form 2.2.5.1-164.1-a Hilbert modular form 2.2.5.1-164.2-a $1 + T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T + 5 T^{2}$ $1 + 6 T^{2} + 49 T^{4}$
4-4112-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-257.1-a Bianchi modular form 2.0.4.1-257.2-a Elliptic curve 2.0.4.1-257.1-a Elliptic curve 2.0.4.1-257.2-a $1 + T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-4136-1.1-c1e2-0-0 Genus 2 curve 4136.a $1 + T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 3 T + 6 T^{2} + 21 T^{3} + 49 T^{4}$
4-4214-1.1-c1e2-0-1 Bianchi modular form 2.0.7.1-86.2-a Bianchi modular form 2.0.7.1-86.3-a Elliptic curve 2.0.7.1-86.2-a Elliptic curve 2.0.7.1-86.3-a $( 1 - T )( 1 - T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T^{2} + 25 T^{4}$ $1 + 4 T + 7 T^{2}$
4-65e2-1.1-c1e2-0-0 Elliptic curve 2.2.65.1-1.1-b Hilbert modular form 2.2.65.1-1.1-b Modular form 65.2.d.a $( 1 + T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $( 1 + 7 T^{2} )^{2}$
4-65e2-1.1-c1e2-0-3 Elliptic curve 2.2.65.1-1.1-a Hilbert modular form 2.2.65.1-1.1-a Modular form 65.2.d.b $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T + 5 T^{2}$ $( 1 + 7 T^{2} )^{2}$
4-4312-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-88.2-a Bianchi modular form 2.0.7.1-88.7-a Elliptic curve 2.0.7.1-88.2-a Elliptic curve 2.0.7.1-88.7-a $1 + T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 7 T^{2}$
4-4331-1.1-c1e2-0-0 Genus 2 curve 4331.a $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $1 + T + 6 T^{2} + 7 T^{3} + 49 T^{4}$
4-4352-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-272.1-a Bianchi modular form 2.0.4.1-272.2-a Elliptic curve 2.0.4.1-272.1-a Elliptic curve 2.0.4.1-272.2-a Genus 2 curve 4352.b $1$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-4528-1.1-c1e2-0-1 Genus 2 curve 4528.a $1 - T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 3 T + 7 T^{2} )( 1 + 7 T^{2} )$
4-68e2-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-16.4-a Elliptic curve 2.2.17.1-16.5-a Hilbert modular form 2.2.17.1-16.4-a Hilbert modular form 2.2.17.1-16.5-a $1 + T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-4672-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-73.1-a Elliptic curve 2.2.8.1-73.2-a Hilbert modular form 2.2.8.1-73.1-a Hilbert modular form 2.2.8.1-73.2-a $1 - 2 T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 + 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-4768-1.1-c1e2-0-0 Genus 2 curve 4768.a $1 + T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 6 T^{2} + 49 T^{4}$
4-4775-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-191.1-a Elliptic curve 2.2.5.1-191.2-a Hilbert modular form 2.2.5.1-191.1-a Hilbert modular form 2.2.5.1-191.2-a $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T + 5 T^{2}$ $1 + 2 T^{2} + 49 T^{4}$
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 $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - T$ $1 - 10 T^{2} + 49 T^{4}$
4-5225-1.1-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-c1e2-0-2 Elliptic curve 2.2.5.1-209.1-a Elliptic curve 2.2.5.1-209.4-a Hilbert modular form 2.2.5.1-209.1-a Hilbert modular form 2.2.5.1-209.4-a $1 + 2 T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 4 T + 5 T^{2}$ $1 + 12 T^{2} + 49 T^{4}$
4-73e2-1.1-c1e2-0-1 Modular form 73.2.d.a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4}$
4-5504-1.1-c1e2-0-0 Genus 2 curve 5504.d $1$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-5674-1.1-c1e2-0-1 Genus 2 curve 5674.b $( 1 + T )( 1 - 2 T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-5888-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-92.1-a Elliptic curve 2.2.8.1-92.2-a Hilbert modular form 2.2.8.1-92.1-a Hilbert modular form 2.2.8.1-92.2-a $1$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 + 7 T^{2} )^{2}$
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 $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 6 T^{2} + 49 T^{4}$
4-6088-1.1-c1e2-0-0 Genus 2 curve 6088.b $1 - T$ $1 - 2 T^{2} + 9 T^{4}$ $1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$ $1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-6107-1.1-c1e2-0-0 Genus 2 curve 6107.a $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - T - 2 T^{2} - 7 T^{3} + 49 T^{4}$
4-6235-1.1-c1e2-0-0 Genus 2 curve 6235.a $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 + T )( 1 - 2 T + 5 T^{2} )$ $1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-6272-1.1-c1e2-0-3 Bianchi modular form 2.0.7.1-128.4-a Bianchi modular form 2.0.7.1-128.5-a Elliptic curve 2.0.7.1-128.4-a Elliptic curve 2.0.7.1-128.5-a $1$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $1 + 7 T^{2}$
4-6343-1.1-c1e2-0-0 Genus 2 curve 6343.a $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-80e2-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-256.1-c Hilbert modular form 2.2.5.1-256.1-c Modular form 80.2.c.a $1$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 10 T^{2} + 49 T^{4}$
4-80e2-1.1-c1e2-0-10 Genus 2 curve 6400.g Modular form 80.2.j.a $1 - 2 T + 2 T^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T + 5 T^{2}$ $1 + 6 T + 18 T^{2} + 42 T^{3} + 49 T^{4}$
4-6560-1.1-c1e2-0-2 Bianchi modular form 2.0.4.1-410.2-a Bianchi modular form 2.0.4.1-410.3-a Elliptic curve 2.0.4.1-410.2-a Elliptic curve 2.0.4.1-410.3-a $1 - T$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-82e2-1.1-c1e2-0-3 Elliptic curve 2.2.41.1-4.1-b Hilbert modular form 2.2.41.1-4.1-b Modular form 82.2.b.b $( 1 - T )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 + 2 T + 5 T^{2} )^{2}$ $1 - 10 T^{2} + 49 T^{4}$
4-6736-1.1-c1e2-0-0 Genus 2 curve 6736.a $1 - T$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - T + 6 T^{2} - 7 T^{3} + 49 T^{4}$
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