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e.g. 3,7,19 e.g. F3=1-T,F5=1+T+5T^2

Results (1-50 of 178 matches)

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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-1660-1.1-c1e2-0-0 Genus 2 curve 1660.a $1 + T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - T )( 1 + 4 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-3887-1.1-c1e2-0-1 Genus 2 curve 3887.a $1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4}$ $( 1 - 3 T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-6520-1.1-c1e2-0-0 Genus 2 curve 6520.a $1 - T$ $1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4}$ $( 1 + T )( 1 - T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-7332-1.1-c1e2-0-0 Genus 2 curve 7332.a $( 1 - T )( 1 + T )$ $( 1 - T )( 1 + T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-10398-1.1-c1e2-0-0 Genus 2 curve 10398.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $( 1 + T )( 1 + T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-13040-1.1-c1e2-0-0 Genus 2 curve 13040.b $1 - T$ $1 - 2 T + 4 T^{2} - 6 T^{3} + 9 T^{4}$ $( 1 - T )( 1 + 3 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-16428-1.1-c1e2-0-1 Elliptic curve 2.2.37.1-12.1-a Elliptic curve 2.2.37.1-12.2-a Hilbert modular form 2.2.37.1-12.1-a Hilbert modular form 2.2.37.1-12.2-a $1 + T^{2}$ $( 1 + T )( 1 - 3 T + 3 T^{2} )$ $1 + 8 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-16820-1.1-c1e2-0-0 Elliptic curve 2.2.29.1-20.1-b Elliptic curve 2.2.29.1-20.2-b Hilbert modular form 2.2.29.1-20.1-b Hilbert modular form 2.2.29.1-20.2-b $1 + T^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 + T )( 1 - T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-17642-1.1-c1e2-0-0 Genus 2 curve 17642.a $( 1 + T )( 1 + 2 T^{2} )$ $( 1 - T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 + 2 T + 8 T^{2} + 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-20205-1.1-c1e2-0-0 Genus 2 curve 20205.a $1 + T^{2} + 4 T^{4}$ $1 + 2 T + 3 T^{2}$ $( 1 + T )( 1 + 2 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-30544-1.1-c1e2-0-0 Genus 2 curve 30544.a $1$ $( 1 + T + 3 T^{2} )^{2}$ $1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-30704-1.1-c1e2-0-0 Genus 2 curve 30704.a $1 + 2 T + 2 T^{2}$ $1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4}$ $( 1 - T + 5 T^{2} )^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-30759-1.1-c1e2-0-0 Genus 2 curve 30759.a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + T + 3 T^{2} )$ $1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-31550-1.1-c1e2-0-0 Genus 2 curve 31550.b $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4}$ $( 1 - T )( 1 + T )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-32890-1.1-c1e2-0-0 Genus 2 curve 32890.a $( 1 + T )( 1 - T + 2 T^{2} )$ $1 + 9 T^{4}$ $( 1 + T )( 1 + 2 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-37976-1.1-c1e2-0-0 Genus 2 curve 37976.a $1 + T$ $( 1 - 2 T + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-39346-1.1-c1e2-0-0 Genus 2 curve 39346.a $( 1 - T )( 1 + 2 T^{2} )$ $1 - T - T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-41925-1.1-c1e2-0-0 Genus 2 curve 41925.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T )( 1 + 2 T + 3 T^{2} )$ $1 + 3 T + 5 T^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-43879-1.1-c1e2-0-0 Genus 2 curve 43879.a $1 + 2 T^{2} + 4 T^{4}$ $1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4}$ $1 + T - T^{2} + 5 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-52272-1.1-c1e2-0-15 Genus 2 curve 52272.e $1 + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-52812-1.1-c1e2-0-2 Genus 2 curve 52812.a $1 + T^{2}$ $1$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-54867-1.1-c1e2-0-0 Genus 2 curve 54867.a $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 - T )( 1 + 3 T + 3 T^{2} )$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-55680-1.1-c1e2-0-0 Genus 2 curve 55680.a $1$ $( 1 + T )( 1 - 2 T + 3 T^{2} )$ $( 1 + T )( 1 + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-61725-1.1-c1e2-0-0 Genus 2 curve 61725.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T )( 1 + 3 T^{2} )$ $( 1 - T )( 1 + T )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-66209-1.1-c1e2-0-0 Genus 2 curve 66209.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T + 3 T^{2} + 3 T^{3} + 9 T^{4}$ $1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-71408-1.1-c1e2-0-0 Genus 2 curve 71408.b $1 - T$ $1 - T - T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-80074-1.1-c1e2-0-0 Genus 2 curve 80074.a $( 1 + T )( 1 + 2 T^{2} )$ $1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-81962-1.1-c1e2-0-0 Genus 2 curve 81962.a $( 1 + T )( 1 + 2 T^{2} )$ $1 - T + T^{2} - 3 T^{3} + 9 T^{4}$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-103680-1.1-c1e2-0-6 Genus 2 curve 103680.b $1$ $1 - 2 T + 3 T^{2}$ $( 1 + T )( 1 + T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-104596-1.1-c1e2-0-0 Genus 2 curve 104596.a $1 + T^{2}$ $( 1 - T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 2 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-104704-1.1-c1e2-0-1 Elliptic curve 2.2.8.1-1636.1-c Elliptic curve 2.2.8.1-1636.2-c Hilbert modular form 2.2.8.1-1636.1-c Hilbert modular form 2.2.8.1-1636.2-c $1$ $1 - T^{2} + 9 T^{4}$ $1 - T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-114808-1.1-c1e2-0-0 Genus 2 curve 114808.a $1 - T$ $1 + 9 T^{4}$ $1 - T - 5 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-114938-1.1-c1e2-0-0 Genus 2 curve 114938.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + T - T^{2} + 3 T^{3} + 9 T^{4}$ $1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-121089-1.1-c1e2-0-0 Genus 2 curve 121089.a $1 + T^{2} + 4 T^{4}$ $( 1 - T )( 1 + 3 T + 3 T^{2} )$ $1 + T + 2 T^{2} + 5 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-123110-1.1-c1e2-0-0 Genus 2 curve 123110.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 + 3 T + 5 T^{2} + 9 T^{3} + 9 T^{4}$ $( 1 + T )( 1 - 2 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-126661-1.1-c1e2-0-0 Genus 2 curve 126661.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + T + T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-134741-1.1-c1e2-0-0 Genus 2 curve 134741.a $1 + 2 T^{2} + 4 T^{4}$ $( 1 - 3 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-136748-1.1-c1e2-0-0 Genus 2 curve 136748.a $1 + T^{2}$ $1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4}$ $1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-154496-1.1-c1e2-0-3 Elliptic curve 2.2.8.1-2414.2-a Elliptic curve 2.2.8.1-2414.3-a Hilbert modular form 2.2.8.1-2414.2-a Hilbert modular form 2.2.8.1-2414.3-a $1 - T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 - 3 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-157776-1.1-c1e2-0-0 Genus 2 curve 157776.a $1 - T + 2 T^{2}$ $( 1 + T )( 1 - 3 T + 3 T^{2} )$ $1 + T + T^{2} + 5 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-169725-1.1-c1e2-0-0 Genus 2 curve 169725.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T )( 1 + T + 3 T^{2} )$ $1 + T + 5 T^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-174987-1.1-c1e2-0-0 Bianchi modular form 2.0.3.1-19443.1-a Bianchi modular form 2.0.3.1-19443.2-a Elliptic curve 2.0.3.1-19443.1-a Elliptic curve 2.0.3.1-19443.2-a $1 - 3 T^{2} + 4 T^{4}$ $1 + T$ $1 - T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-176084-1.1-c1e2-0-0 Genus 2 curve 176084.b $( 1 - T )( 1 + T )$ $1 + 9 T^{4}$ $1 + T + 3 T^{2} + 5 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-178400-1.1-c1e2-0-0 Genus 2 curve 178400.a $1 - T$ $( 1 - 3 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $1 + 5 T^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-179789-1.1-c1e2-0-0 Genus 2 curve 179789.a $1 + T^{2} + 4 T^{4}$ $1 - T + T^{2} - 3 T^{3} + 9 T^{4}$ $1 - T + 3 T^{2} - 5 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-180160-1.1-c1e2-0-0 Genus 2 curve 180160.a $1$ $( 1 - 2 T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 + T )( 1 + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-182528-1.1-c1e2-0-0 Genus 2 curve 182528.a $1$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-187197-1.1-c1e2-0-0 Genus 2 curve 187197.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 - T )( 1 + T + 3 T^{2} )$ $1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-196278-1.1-c1e2-0-0 Genus 2 curve 196278.a $( 1 + T )( 1 - T + 2 T^{2} )$ $( 1 - T )( 1 + 2 T + 3 T^{2} )$ $1 - 2 T + 5 T^{2} - 10 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-198320-1.1-c1e2-0-0 Genus 2 curve 198320.a $1 + 2 T + 2 T^{2}$ $( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$ $( 1 - T )( 1 + 5 T^{2} )$ $( 1 - 5 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
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