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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-5592-1.1-c1e2-0-0 Genus 2 curve 5592.a $1 + 2 T^{2}$ $( 1 + T )( 1 + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-5630-1.1-c1e2-0-0 Genus 2 curve 5630.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + T + 3 T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 + T )( 1 + 4 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-6282-1.1-c1e2-0-0 Genus 2 curve 6282.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 + T + T^{2}$ $1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-7209-1.1-c1e2-0-1 Genus 2 curve 7209.a $1 + 2 T^{2} + 4 T^{4}$ $1 + T + 3 T^{2}$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-11360-1.1-c1e2-0-0 Genus 2 curve 11360.a $1$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + T )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-14450-1.1-c1e2-0-2 Elliptic curve 2.2.17.1-50.1-c Elliptic curve 2.2.17.1-50.2-c Hilbert modular form 2.2.17.1-50.1-c Hilbert modular form 2.2.17.1-50.2-c $( 1 - T )( 1 - 2 T + 2 T^{2} )$ $1 + 4 T^{2} + 9 T^{4}$ $( 1 - T )( 1 + T )$ $1 + 3 T^{2} + 49 T^{4}$
4-17061-1.1-c1e2-0-1 Genus 2 curve 17061.b $1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4}$ $( 1 - T )( 1 + 3 T^{2} )$ $( 1 - 3 T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-19375-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-775.1-d Elliptic curve 2.2.5.1-775.2-d Hilbert modular form 2.2.5.1-775.1-d Hilbert modular form 2.2.5.1-775.2-d $1 - 2 T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1$ $1 + 3 T^{2} + 49 T^{4}$
4-20471-1.1-c1e2-0-0 Genus 2 curve 20471.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 + T + 3 T^{2} )^{2}$ $1 + 3 T + 7 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-20672-1.1-c1e2-0-0 Bianchi modular form 2.0.8.1-323.1-a Bianchi modular form 2.0.8.1-323.4-a Elliptic curve 2.0.8.1-323.1-a Elliptic curve 2.0.8.1-323.4-a $1 + T + 2 T^{2}$ $( 1 - 3 T + 3 T^{2} )( 1 - 2 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-21968-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-1373.1-a Bianchi modular form 2.0.4.1-1373.2-a Elliptic curve 2.0.4.1-1373.1-a Elliptic curve 2.0.4.1-1373.2-a $1 + T + 2 T^{2}$ $1 - 4 T^{2} + 9 T^{4}$ $( 1 + 2 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-155e2-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-961.1-b Elliptic curve 2.2.5.1-961.1-d Hilbert modular form 2.2.5.1-961.1-b Hilbert modular form 2.2.5.1-961.1-d $1 - 2 T^{2} + 4 T^{4}$ $1 + 3 T^{2} + 9 T^{4}$ $1 - 3 T + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-29403-1.1-c1e2-0-0 Bianchi modular form 2.0.11.1-243.2-a Bianchi modular form 2.0.11.1-243.5-a Elliptic curve 2.0.11.1-243.2-a Elliptic curve 2.0.11.1-243.5-a $1 + 2 T^{2} + 4 T^{4}$ $1 + T$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-34100-1.1-c1e2-0-10 Elliptic curve 2.2.5.1-1364.1-f Elliptic curve 2.2.5.1-1364.4-f Hilbert modular form 2.2.5.1-1364.1-f Hilbert modular form 2.2.5.1-1364.4-f $( 1 - T )( 1 + T )$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-36443-1.1-c1e2-0-0 Genus 2 curve 36443.a $1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4}$ $1 + 3 T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-36882-1.1-c1e2-0-1 Genus 2 curve 36882.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + T + 3 T^{2}$ $1 + 7 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-36914-1.1-c1e2-0-0 Genus 2 curve 36914.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 - T^{2} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-40100-1.1-c1e2-0-2 Elliptic curve 2.2.5.1-1604.1-c Elliptic curve 2.2.5.1-1604.2-c Hilbert modular form 2.2.5.1-1604.1-c Hilbert modular form 2.2.5.1-1604.2-c $1 + T^{2}$ $1 + 4 T^{2} + 9 T^{4}$ $1 - T + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-40528-1.1-c1e2-0-0 Genus 2 curve 40528.a $1$ $1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4}$ $1 + 5 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-41236-1.1-c1e2-0-2 Elliptic curve 2.2.13.1-244.1-f Elliptic curve 2.2.13.1-244.2-f Hilbert modular form 2.2.13.1-244.1-f Hilbert modular form 2.2.13.1-244.2-f $( 1 - T )( 1 + T )$ $( 1 + T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 + 3 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-44794-1.1-c1e2-0-0 Genus 2 curve 44794.c $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$ $1 + 3 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-48509-1.1-c1e2-0-0 Genus 2 curve 48509.a $1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + 2 T + T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 3 T + 11 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-50483-1.1-c1e2-0-0 Genus 2 curve 50483.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 + T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 + 2 T + 8 T^{2} + 10 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-51386-1.1-c1e2-0-0 Genus 2 curve 51386.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + 2 T + 5 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-52272-1.1-c1e2-0-11 Elliptic curve 2.2.12.1-363.2-c Elliptic curve 2.2.12.1-363.3-c Hilbert modular form 2.2.12.1-363.2-c Hilbert modular form 2.2.12.1-363.3-c $1 + 2 T + 2 T^{2}$ $1 + T$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-52272-1.1-c1e2-0-13 Elliptic curve 2.2.12.1-363.2-b Elliptic curve 2.2.12.1-363.3-b Hilbert modular form 2.2.12.1-363.2-b Hilbert modular form 2.2.12.1-363.3-b $1 - 2 T + 2 T^{2}$ $1 - T$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-54332-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-188.3-a Elliptic curve 2.2.17.1-188.6-a Hilbert modular form 2.2.17.1-188.3-a Hilbert modular form 2.2.17.1-188.6-a $1 + 2 T + 2 T^{2}$ $1 - T^{2} + 9 T^{4}$ $1 + 8 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-55075-1.1-c1e2-0-0 Genus 2 curve 55075.a $( 1 - 2 T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-55360-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-3460.1-a Bianchi modular form 2.0.4.1-3460.4-a Elliptic curve 2.0.4.1-3460.1-a Elliptic curve 2.0.4.1-3460.4-a $1$ $1 + T^{2} + 9 T^{4}$ $( 1 - T )( 1 + 2 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-55666-1.1-c1e2-0-0 Genus 2 curve 55666.a $( 1 + T )( 1 + T + 2 T^{2} )$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-55815-1.1-c1e2-0-2 Elliptic curve 2.2.61.1-15.2-b Elliptic curve 2.2.61.1-15.3-b Hilbert modular form 2.2.61.1-15.2-b Hilbert modular form 2.2.61.1-15.3-b $1 + T^{2} + 4 T^{4}$ $( 1 - T )( 1 - 3 T + 3 T^{2} )$ $( 1 - T )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-56009-1.1-c1e2-0-0 Genus 2 curve 56009.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + 3 T + 5 T^{2} + 9 T^{3} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-60100-1.1-c1e2-0-3 Elliptic curve 2.2.5.1-2404.1-c Elliptic curve 2.2.5.1-2404.2-c Hilbert modular form 2.2.5.1-2404.1-c Hilbert modular form 2.2.5.1-2404.2-c $1 + T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + T + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-61757-1.1-c1e2-0-0 Genus 2 curve 61757.a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-62752-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-3922.1-a Bianchi modular form 2.0.4.1-3922.4-a Elliptic curve 2.0.4.1-3922.1-a Elliptic curve 2.0.4.1-3922.4-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-62752-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-3922.1-b Bianchi modular form 2.0.4.1-3922.4-c Elliptic curve 2.0.4.1-3922.1-b Elliptic curve 2.0.4.1-3922.4-c $1 - T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-62784-1.1-c1e2-0-0 Elliptic curve 2.2.12.1-436.1-b Elliptic curve 2.2.12.1-436.2-b Hilbert modular form 2.2.12.1-436.1-b Hilbert modular form 2.2.12.1-436.2-b $1$ $1 + T + 3 T^{2}$ $1 + 7 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-62784-1.1-c1e2-0-1 Elliptic curve 2.2.12.1-436.1-a Elliptic curve 2.2.12.1-436.2-a Hilbert modular form 2.2.12.1-436.1-a Hilbert modular form 2.2.12.1-436.2-a $1$ $1 - T + 3 T^{2}$ $1 + 7 T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-63904-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-3994.1-a Bianchi modular form 2.0.4.1-3994.2-a Elliptic curve 2.0.4.1-3994.1-a Elliptic curve 2.0.4.1-3994.2-a $1 + T$ $1 + 4 T^{2} + 9 T^{4}$ $( 1 + 3 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-64447-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-223.1-a Elliptic curve 2.2.17.1-223.2-a Hilbert modular form 2.2.17.1-223.1-a Hilbert modular form 2.2.17.1-223.2-a $( 1 + 2 T^{2} )^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-64775-1.1-c1e2-0-3 Elliptic curve 2.2.5.1-2591.1-a Elliptic curve 2.2.5.1-2591.2-a Hilbert modular form 2.2.5.1-2591.1-a Hilbert modular form 2.2.5.1-2591.2-a $1 - T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-65725-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-2629.1-a Elliptic curve 2.2.5.1-2629.4-a Hilbert modular form 2.2.5.1-2629.1-a Hilbert modular form 2.2.5.1-2629.4-a $1 - 3 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-65988-1.1-c1e2-0-0 Genus 2 curve 65988.c $1 + T^{2}$ $1 + T + 3 T^{2}$ $1 - T^{2} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-66592-1.1-c1e2-0-0 Genus 2 curve 66592.a $1$ $1 - 2 T + 4 T^{2} - 6 T^{3} + 9 T^{4}$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-68275-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-2731.1-c Elliptic curve 2.2.5.1-2731.2-c Hilbert modular form 2.2.5.1-2731.1-c Hilbert modular form 2.2.5.1-2731.2-c $1 - 3 T^{2} + 4 T^{4}$ $1 - T^{2} + 9 T^{4}$ $1 - 2 T + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-69393-1.1-c1e2-0-0 Genus 2 curve 69393.a $1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$ $( 1 + T )( 1 + 2 T + 3 T^{2} )$ $1 + 2 T + 10 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-73624-1.1-c1e2-0-0 Genus 2 curve 73624.b $1 + T$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + 4 T + 9 T^{2} + 20 T^{3} + 25 T^{4}$ $1 + 3 T^{2} + 49 T^{4}$
4-74525-1.1-c1e2-0-3 Elliptic curve 2.2.5.1-2981.1-b Elliptic curve 2.2.5.1-2981.4-b Hilbert modular form 2.2.5.1-2981.1-b Hilbert modular form 2.2.5.1-2981.4-b $1 - T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 5 T^{2}$ $1 + 3 T^{2} + 49 T^{4}$
4-74560-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-4660.1-b Bianchi modular form 2.0.4.1-4660.4-b Elliptic curve 2.0.4.1-4660.1-b Elliptic curve 2.0.4.1-4660.4-b $1$ $1 + 9 T^{4}$ $( 1 - T )( 1 + 3 T + 5 T^{2} )$ $1 + 3 T^{2} + 49 T^{4}$
4-74875-1.1-c1e2-0-5 Elliptic curve 2.2.5.1-2995.1-d Elliptic curve 2.2.5.1-2995.2-d Hilbert modular form 2.2.5.1-2995.1-d Hilbert modular form 2.2.5.1-2995.2-d $1 + T^{2} + 4 T^{4}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - T$ $1 + 3 T^{2} + 49 T^{4}$
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