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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-13e2-1.1-c1e2-0-0 Genus 2 curve 169.a Modular form 13.2.e.a $1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$ $1 + 2 T + T^{2} + 6 T^{3} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 7 T^{2} + 49 T^{4}$
4-4171-1.1-c1e2-0-0 Genus 2 curve 4171.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $1 + T + 3 T^{2} + 3 T^{3} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-6688-1.1-c1e2-0-2 Genus 2 curve 6688.a $1$ $( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-11179-1.1-c1e2-0-0 Genus 2 curve 11179.a $1 + 2 T^{2} + 4 T^{4}$ $1 + 4 T^{2} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + T )( 1 + 3 T + 7 T^{2} )$
4-12564-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-1396.1-b Bianchi modular form 2.0.3.1-1396.2-b Elliptic curve 2.0.3.1-1396.1-b Elliptic curve 2.0.3.1-1396.2-b $( 1 - T )( 1 + T )$ $1 + 2 T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-13568-1.1-c1e2-0-2 Genus 2 curve 13568.b $1 + T + 2 T^{2}$ $1 + 2 T + T^{2} + 6 T^{3} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-117e2-1.1-c1e2-0-17 Modular form 117.2.q.c $1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4}$ $1$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 7 T^{2} + 49 T^{4}$
4-14284-1.1-c1e2-0-0 Genus 2 curve 14284.a $1 + T + T^{2}$ $( 1 - T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $1 - 5 T^{2} + 49 T^{4}$
4-18507-1.1-c1e2-0-0 Genus 2 curve 18507.b $1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$ $( 1 - T )( 1 + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $1 + T - 2 T^{2} + 7 T^{3} + 49 T^{4}$
4-19328-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-302.1-a Elliptic curve 2.2.8.1-302.2-a Hilbert modular form 2.2.8.1-302.1-a Hilbert modular form 2.2.8.1-302.2-a $1 + T$ $1 - T^{2} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-21339-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-2371.1-a Bianchi modular form 2.0.3.1-2371.2-a Elliptic curve 2.0.3.1-2371.1-a Elliptic curve 2.0.3.1-2371.2-a $1 - T^{2} + 4 T^{4}$ $1 + T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-156e2-1.1-c1e2-0-13 Modular form 156.2.q.a $1$ $1 - T + T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-24704-1.1-c1e2-0-5 Elliptic curve 2.2.8.1-386.1-d Elliptic curve 2.2.8.1-386.2-d Hilbert modular form 2.2.8.1-386.1-d Hilbert modular form 2.2.8.1-386.2-d $1 - T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-24768-1.1-c1e2-0-0 Bianchi modular form 2.0.8.1-387.2-a Bianchi modular form 2.0.8.1-387.5-a Elliptic curve 2.0.8.1-387.2-a Elliptic curve 2.0.8.1-387.5-a $1 + 2 T + 2 T^{2}$ $1 + 3 T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $1 - 8 T^{2} + 49 T^{4}$
4-13e4-1.1-c1e2-0-0 Modular form 169.2.e.a $1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4}$ $1 + 2 T + T^{2} + 6 T^{3} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 7 T^{2} + 49 T^{4}$
4-13e4-1.1-c1e2-0-3 Elliptic curve 2.2.13.1-169.1-a Hilbert modular form 2.2.13.1-169.1-a Modular form 169.2.b.a $1 - T^{2} + 4 T^{4}$ $( 1 - 2 T + 3 T^{2} )^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 7 T^{2} )^{2}$
4-30807-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-3423.1-a Bianchi modular form 2.0.3.1-3423.4-a Elliptic curve 2.0.3.1-3423.1-a Elliptic curve 2.0.3.1-3423.4-a $1 + 2 T^{2} + 4 T^{4}$ $1 + T$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + T + 7 T^{2} )$
4-30848-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-482.1-b Elliptic curve 2.2.8.1-482.2-b Hilbert modular form 2.2.8.1-482.1-b Hilbert modular form 2.2.8.1-482.2-b $1 + T$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 3 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-31356-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-3484.1-a Bianchi modular form 2.0.3.1-3484.4-a Elliptic curve 2.0.3.1-3484.1-a Elliptic curve 2.0.3.1-3484.4-a $( 1 - T )( 1 + T )$ $1 + T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-33024-1.1-c1e2-0-2 Bianchi modular form 2.0.8.1-516.2-a Bianchi modular form 2.0.8.1-516.3-a Elliptic curve 2.0.8.1-516.2-a Elliptic curve 2.0.8.1-516.3-a $1$ $( 1 - T )( 1 + T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 8 T^{2} + 49 T^{4}$
4-33516-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-3724.3-a Bianchi modular form 2.0.3.1-3724.4-a Elliptic curve 2.0.3.1-3724.3-a Elliptic curve 2.0.3.1-3724.4-a $1 + T^{2}$ $1 + T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - T )( 1 + T )$
4-33876-1.1-c1e2-0-0 Genus 2 curve 33876.a $1 + T + T^{2}$ $1 + T + T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + T + 7 T^{2} + 7 T^{3} + 49 T^{4}$
4-34848-1.1-c1e2-0-11 Elliptic curve 2.2.33.1-32.5-a Elliptic curve 2.2.33.1-32.6-a Hilbert modular form 2.2.33.1-32.5-a Hilbert modular form 2.2.33.1-32.6-a $1 - 2 T + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 6 T^{2} + 49 T^{4}$
4-34848-1.1-c1e2-0-14 Elliptic curve 2.2.33.1-32.5-f Elliptic curve 2.2.33.1-32.6-f Hilbert modular form 2.2.33.1-32.5-f Hilbert modular form 2.2.33.1-32.6-f $1 + 2 T + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 6 T^{2} + 49 T^{4}$
4-36389-1.1-c1e2-0-0 Genus 2 curve 36389.a $1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 3 T + 11 T^{2} + 21 T^{3} + 49 T^{4}$
4-36736-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-574.2-e Elliptic curve 2.2.8.1-574.3-e Hilbert modular form 2.2.8.1-574.2-e Hilbert modular form 2.2.8.1-574.3-e $1 + T$ $1 - T^{2} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + T )( 1 - 4 T + 7 T^{2} )$
4-37349-1.1-c1e2-0-0 Elliptic curve 2.2.13.1-221.1-c Elliptic curve 2.2.13.1-221.2-c Hilbert modular form 2.2.13.1-221.1-c Hilbert modular form 2.2.13.1-221.2-c $1 - T^{2} + 4 T^{4}$ $( 1 + 2 T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $1 - T^{2} + 49 T^{4}$
4-40608-1.1-c1e2-0-0 Elliptic curve 2.2.12.1-282.1-b Elliptic curve 2.2.12.1-282.2-b Hilbert modular form 2.2.12.1-282.1-b Hilbert modular form 2.2.12.1-282.2-b $1 - T$ $1 + T$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-40608-1.1-c1e2-0-7 Elliptic curve 2.2.12.1-282.1-e Elliptic curve 2.2.12.1-282.2-e Hilbert modular form 2.2.12.1-282.1-e Hilbert modular form 2.2.12.1-282.2-e $1 + T$ $1 - T$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-40932-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-4548.1-a Bianchi modular form 2.0.3.1-4548.2-a Elliptic curve 2.0.3.1-4548.1-a Elliptic curve 2.0.3.1-4548.2-a $1 + T^{2}$ $1 - T$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-41236-1.1-c1e2-0-1 Elliptic curve 2.2.13.1-244.1-c Elliptic curve 2.2.13.1-244.2-c Hilbert modular form 2.2.13.1-244.1-c Hilbert modular form 2.2.13.1-244.2-c $1 + T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-42129-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-4681.2-a Bianchi modular form 2.0.3.1-4681.3-a Elliptic curve 2.0.3.1-4681.2-a Elliptic curve 2.0.3.1-4681.3-a $1 + 2 T^{2} + 4 T^{4}$ $1 + 2 T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-208e2-1.1-c1e2-0-8 Modular form 208.2.w.b $1$ $1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 7 T^{2} + 49 T^{4}$
4-44536-1.1-c1e2-0-0 Genus 2 curve 44536.a $1 - T$ $1 + T + 3 T^{2} + 3 T^{3} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + T - 7 T^{2} + 7 T^{3} + 49 T^{4}$
4-46016-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-719.1-c Elliptic curve 2.2.8.1-719.2-c Hilbert modular form 2.2.8.1-719.1-c Hilbert modular form 2.2.8.1-719.2-c $1 + 2 T + 2 T^{2}$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-47988-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-5332.1-a Bianchi modular form 2.0.3.1-5332.4-a Elliptic curve 2.0.3.1-5332.1-a Elliptic curve 2.0.3.1-5332.4-a $1 + T^{2}$ $1 - T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-50048-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-782.1-c Elliptic curve 2.2.8.1-782.4-c Hilbert modular form 2.2.8.1-782.1-c Hilbert modular form 2.2.8.1-782.4-c $1 - T$ $1 + T^{2} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-50409-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-5601.1-a Bianchi modular form 2.0.3.1-5601.2-a Elliptic curve 2.0.3.1-5601.1-a Elliptic curve 2.0.3.1-5601.2-a $1 + T^{2} + 4 T^{4}$ $1 - T$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-234e2-1.1-c1e2-0-12 Elliptic curve 2.2.13.1-324.4-a Elliptic curve 2.2.13.1-324.5-a Hilbert modular form 2.2.13.1-324.4-a Hilbert modular form 2.2.13.1-324.5-a $1 + T^{2}$ $1 - 2 T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-55424-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-866.1-b Elliptic curve 2.2.8.1-866.2-b Hilbert modular form 2.2.8.1-866.1-b Hilbert modular form 2.2.8.1-866.2-b $1 - T$ $1 + T^{2} + 9 T^{4}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-55762-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-1138.1-a Bianchi modular form 2.0.7.1-1138.4-a Elliptic curve 2.0.7.1-1138.1-a Elliptic curve 2.0.7.1-1138.4-a $( 1 + T )( 1 + T + 2 T^{2} )$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 3 T + 7 T^{2}$
4-57249-1.1-c1e2-0-1 Bianchi modular form 2.0.3.1-6361.1-a Bianchi modular form 2.0.3.1-6361.2-a Elliptic curve 2.0.3.1-6361.1-a Elliptic curve 2.0.3.1-6361.2-a $1 - T^{2} + 4 T^{4}$ $1 - T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-57276-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-6364.2-b Bianchi modular form 2.0.3.1-6364.3-b Elliptic curve 2.0.3.1-6364.2-b Elliptic curve 2.0.3.1-6364.3-b $1 + T^{2}$ $1 - 2 T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )^{2}$
4-39e3-1.1-c1e2-0-1 Elliptic curve 2.2.13.1-351.3-g Elliptic curve 2.2.13.1-351.4-g Hilbert modular form 2.2.13.1-351.3-g Hilbert modular form 2.2.13.1-351.4-g $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-39e3-1.1-c1e2-0-13 Elliptic curve 2.2.13.1-351.3-a Elliptic curve 2.2.13.1-351.4-a Hilbert modular form 2.2.13.1-351.3-a Hilbert modular form 2.2.13.1-351.4-a $1 - T^{2} + 4 T^{4}$ $1 + T + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $1 + 4 T^{2} + 49 T^{4}$
4-39e3-1.1-c1e2-0-2 Elliptic curve 2.2.13.1-351.3-b Elliptic curve 2.2.13.1-351.4-b Hilbert modular form 2.2.13.1-351.3-b Hilbert modular form 2.2.13.1-351.4-b $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $1 - 10 T^{2} + 49 T^{4}$
4-59534-1.1-c1e2-0-2 Elliptic curve 2.2.17.1-206.1-a Elliptic curve 2.2.17.1-206.4-a Hilbert modular form 2.2.17.1-206.1-a Hilbert modular form 2.2.17.1-206.4-a $( 1 - T )( 1 - 2 T + 2 T^{2} )$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-60021-1.1-c1e2-0-5 Bianchi modular form 2.0.3.1-6669.1-b Bianchi modular form 2.0.3.1-6669.4-b Elliptic curve 2.0.3.1-6669.1-b Elliptic curve 2.0.3.1-6669.4-b $1 + T^{2} + 4 T^{4}$ $1$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-61952-1.1-c1e2-0-2 Bianchi modular form 2.0.8.1-968.2-b Bianchi modular form 2.0.8.1-968.2-c Elliptic curve 2.0.8.1-968.2-b Elliptic curve 2.0.8.1-968.2-c $1$ $( 1 - T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-65664-1.1-c1e2-0-17 Bianchi modular form 2.0.8.1-1026.1-c Bianchi modular form 2.0.8.1-1026.8-c Elliptic curve 2.0.8.1-1026.1-c Elliptic curve 2.0.8.1-1026.8-c $1 - T$ $1 + 3 T^{2}$ $1 - 7 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
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