L-function Euler product search

Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank
Degree	Bad \(p\)	Root analytic conductor	Motivic weight	Spectral label
Root number	Primitive	Origin	Exclude origin

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Columns to display		Euler factor constraints
	e.g. 3,7,19		e.g. F3=1-T,F5=1+T+5T^2

Results (1-50 of )

		$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label	Origin	\(F_{ 2 }(T)\)	\(F_{ 3 }(T)\)	\(F_{ 5 }(T)\)	\(F_{ 7 }(T)\)
2-17-1.1-c1-0-0	Elliptic curve 17.a Modular form 17.2.a.a Modular form 17.2.a.a.1.1	$1 + T + 2 T^{2}$	$1 + 3 T^{2}$	$1 + 2 T + 5 T^{2}$	$1 - 4 T + 7 T^{2}$
2-2e5-1.1-c1-0-0	Elliptic curve 32.a Modular form 32.2.a.a Modular form 32.2.a.a.1.1	$1$	$1 + 3 T^{2}$	$1 + 2 T + 5 T^{2}$	$1 + 7 T^{2}$
2-40-1.1-c1-0-0	Elliptic curve 40.a Modular form 40.2.a.a Modular form 40.2.a.a.1.1	$1$	$1 + 3 T^{2}$	$1 - T$	$1 + 4 T + 7 T^{2}$
2-46-1.1-c1-0-0	Elliptic curve 46.a Modular form 46.2.a.a Modular form 46.2.a.a.1.1	$1 + T$	$1 + 3 T^{2}$	$1 - 4 T + 5 T^{2}$	$1 + 4 T + 7 T^{2}$
2-7e2-1.1-c1-0-0	Elliptic curve 49.a Modular form 49.2.a.a Modular form 49.2.a.a.1.1	$1 - T + 2 T^{2}$	$1 + 3 T^{2}$	$1 + 5 T^{2}$	$1$
2-52-1.1-c1-0-0	Elliptic curve 52.a Modular form 52.2.a.a Modular form 52.2.a.a.1.1	$1$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 + 2 T + 7 T^{2}$
2-55-1.1-c1-0-1	Elliptic curve 55.a Modular form 55.2.a.a Modular form 55.2.a.a.1.1	$1 - T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - T$	$1 + 7 T^{2}$
2-56-1.1-c1-0-0	Elliptic curve 56.a Modular form 56.2.a.a Modular form 56.2.a.a.1.1	$1$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 + T$
2-62-1.1-c1-0-2	Elliptic curve 62.a Modular form 62.2.a.a Modular form 62.2.a.a.1.1	$1 - T$	$1 + 3 T^{2}$	$1 + 2 T + 5 T^{2}$	$1 + 7 T^{2}$
2-2e6-1.1-c1-0-0	Elliptic curve 64.a Modular form 64.2.a.a Modular form 64.2.a.a.1.1	$1$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 + 7 T^{2}$
2-70-1.1-c1-0-0	Elliptic curve 70.a Modular form 70.2.a.a Modular form 70.2.a.a.1.1	$1 - T$	$1 + 3 T^{2}$	$1 + T$	$1 + T$
2-73-1.1-c1-0-1	Elliptic curve 73.a Modular form 73.2.a.a Modular form 73.2.a.a.1.1	$1 - T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 - 2 T + 7 T^{2}$
2-80-1.1-c1-0-0	Elliptic curve 80.a Modular form 80.2.a.a Modular form 80.2.a.a.1.1	$1$	$1 + 3 T^{2}$	$1 - T$	$1 - 4 T + 7 T^{2}$
2-91-1.1-c1-0-4	Elliptic curve 91.a Modular form 91.2.a.a Modular form 91.2.a.a.1.1	$1 + 2 T + 2 T^{2}$	$1 + 3 T^{2}$	$1 + 3 T + 5 T^{2}$	$1 + T$
2-94-1.1-c1-0-2	Elliptic curve 94.a Modular form 94.2.a.a Modular form 94.2.a.a.1.1	$1 - T$	$1 + 3 T^{2}$	$1 + 5 T^{2}$	$1 + 7 T^{2}$
2-109-1.1-c1-0-2	Elliptic curve 109.a Modular form 109.2.a.a Modular form 109.2.a.a.1.1	$1 - T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - 3 T + 5 T^{2}$	$1 - 2 T + 7 T^{2}$
2-112-1.1-c1-0-0	Elliptic curve 112.b Modular form 112.2.a.b Modular form 112.2.a.b.1.1	$1$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 - T$
2-115-1.1-c1-0-4	Elliptic curve 115.a Modular form 115.2.a.a Modular form 115.2.a.a.1.1	$1 - 2 T + 2 T^{2}$	$1 + 3 T^{2}$	$1 + T$	$1 - T + 7 T^{2}$
2-124-1.1-c1-0-0	Elliptic curve 124.b Modular form 124.2.a.b Modular form 124.2.a.b.1.1	$1$	$1 + 3 T^{2}$	$1 - T + 5 T^{2}$	$1 - 3 T + 7 T^{2}$
2-130-1.1-c1-0-0	Elliptic curve 130.b Modular form 130.2.a.b Modular form 130.2.a.b.1.1	$1 - T$	$1 + 3 T^{2}$	$1 - T$	$1 + 7 T^{2}$
2-142-1.1-c1-0-0	Elliptic curve 142.b Modular form 142.2.a.b Modular form 142.2.a.b.1.1	$1 + T$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 + 7 T^{2}$
2-145-1.1-c1-0-7	Elliptic curve 145.a Modular form 145.2.a.a Modular form 145.2.a.a.1.1	$1 + T + 2 T^{2}$	$1 + 3 T^{2}$	$1 + T$	$1 + 2 T + 7 T^{2}$
2-154-1.1-c1-0-2	Elliptic curve 154.c Modular form 154.2.a.c Modular form 154.2.a.c.1.1	$1 - T$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 + T$
2-154-1.1-c1-0-4	Elliptic curve 154.a Modular form 154.2.a.a Modular form 154.2.a.a.1.1	$1 + T$	$1 + 3 T^{2}$	$1 + 4 T + 5 T^{2}$	$1 + T$
2-161-1.1-c1-0-2	Elliptic curve 161.a Modular form 161.2.a.a Modular form 161.2.a.a.1.1	$1 + T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 - T$
2-163-1.1-c1-0-10	Elliptic curve 163.a Modular form 163.2.a.a Modular form 163.2.a.a.1.1	$1 + 2 T^{2}$	$1 + 3 T^{2}$	$1 + 4 T + 5 T^{2}$	$1 - 2 T + 7 T^{2}$
2-179-1.1-c1-0-10	Elliptic curve 179.a Modular form 179.2.a.a Modular form 179.2.a.a.1.1	$1 - 2 T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - 3 T + 5 T^{2}$	$1 + 4 T + 7 T^{2}$
2-182-1.1-c1-0-2	Elliptic curve 182.c Modular form 182.2.a.c Modular form 182.2.a.c.1.1	$1 - T$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 + T$
2-184-1.1-c1-0-1	Elliptic curve 184.c Modular form 184.2.a.c Modular form 184.2.a.c.1.1	$1$	$1 + 3 T^{2}$	$1 + 5 T^{2}$	$1 - 4 T + 7 T^{2}$
2-187-1.1-c1-0-7	Elliptic curve 187.b Modular form 187.2.a.b Modular form 187.2.a.b.1.1	$1 - 2 T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - 4 T + 5 T^{2}$	$1 + 5 T + 7 T^{2}$
2-194-1.1-c1-0-6	Elliptic curve 194.a Modular form 194.2.a.a Modular form 194.2.a.a.1.1	$1 - T$	$1 + 3 T^{2}$	$1 - 4 T + 5 T^{2}$	$1 + 4 T + 7 T^{2}$
2-197-1.1-c1-0-8	Elliptic curve 197.a Modular form 197.2.a.a Modular form 197.2.a.a.1.1	$1 + 2 T + 2 T^{2}$	$1 + 3 T^{2}$	$1 + 5 T^{2}$	$1 + 3 T + 7 T^{2}$
2-200-1.1-c1-0-1	Elliptic curve 200.c Modular form 200.2.a.c Modular form 200.2.a.c.1.1	$1$	$1 + 3 T^{2}$	$1$	$1 - 4 T + 7 T^{2}$
2-202-1.1-c1-0-1	Elliptic curve 202.a Modular form 202.2.a.a Modular form 202.2.a.a.1.1	$1 + T$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 - T + 7 T^{2}$
2-205-1.1-c1-0-8	Elliptic curve 205.a Modular form 205.2.a.a Modular form 205.2.a.a.1.1	$1 + T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - T$	$1 + 4 T + 7 T^{2}$
2-208-1.1-c1-0-1	Elliptic curve 208.c Modular form 208.2.a.c Modular form 208.2.a.c.1.1	$1$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 - 2 T + 7 T^{2}$
2-215-1.1-c1-0-14	Elliptic curve 215.a Modular form 215.2.a.a Modular form 215.2.a.a.1.1	$1 + 2 T^{2}$	$1 + 3 T^{2}$	$1 + T$	$1 + 2 T + 7 T^{2}$
2-221-1.1-c1-0-3	Elliptic curve 221.a Modular form 221.2.a.a Modular form 221.2.a.a.1.1	$1 + T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - 4 T + 5 T^{2}$	$1 + 2 T + 7 T^{2}$
2-238-1.1-c1-0-2	Elliptic curve 238.d Modular form 238.2.a.d Modular form 238.2.a.d.1.1	$1 - T$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 - T$
2-238-1.1-c1-0-5	Elliptic curve 238.a Modular form 238.2.a.a Modular form 238.2.a.a.1.1	$1 + T$	$1 + 3 T^{2}$	$1 + 2 T + 5 T^{2}$	$1 + T$
2-244-1.1-c1-0-4	Elliptic curve 244.a Modular form 244.2.a.a Modular form 244.2.a.a.1.1	$1$	$1 + 3 T^{2}$	$1 + 3 T + 5 T^{2}$	$1 + 3 T + 7 T^{2}$
2-248-1.1-c1-0-7	Elliptic curve 248.c Modular form 248.2.a.c Modular form 248.2.a.c.1.1	$1$	$1 + 3 T^{2}$	$1 + 3 T + 5 T^{2}$	$1 + 3 T + 7 T^{2}$
2-254-1.1-c1-0-6	Elliptic curve 254.d Modular form 254.2.a.d Modular form 254.2.a.d.1.1	$1 - T$	$1 + 3 T^{2}$	$1 - 2 T + 5 T^{2}$	$1 + 7 T^{2}$
2-254-1.1-c1-0-9	Elliptic curve 254.a Modular form 254.2.a.a Modular form 254.2.a.a.1.1	$1 + T$	$1 + 3 T^{2}$	$1 + T + 5 T^{2}$	$1 + 3 T + 7 T^{2}$
2-2e8-1.1-c1-0-1	Elliptic curve 256.c Modular form 256.2.a.c Modular form 256.2.a.c.1.1	$1$	$1 + 3 T^{2}$	$1 - 4 T + 5 T^{2}$	$1 + 7 T^{2}$
2-2e8-1.1-c1-0-5	Elliptic curve 256.b Modular form 256.2.a.b Modular form 256.2.a.b.1.1	$1$	$1 + 3 T^{2}$	$1 + 4 T + 5 T^{2}$	$1 + 7 T^{2}$
2-259-1.1-c1-0-7	Elliptic curve 259.a Modular form 259.2.a.a Modular form 259.2.a.a.1.1	$1 - T + 2 T^{2}$	$1 + 3 T^{2}$	$1 - 4 T + 5 T^{2}$	$1 - T$
2-262-1.1-c1-0-7	Elliptic curve 262.a Modular form 262.2.a.a Modular form 262.2.a.a.1.1	$1 + T$	$1 + 3 T^{2}$	$1 + 5 T^{2}$	$1 + 5 T + 7 T^{2}$
2-265-1.1-c1-0-8	Elliptic curve 265.a Modular form 265.2.a.a Modular form 265.2.a.a.1.1	$1 + T + 2 T^{2}$	$1 + 3 T^{2}$	$1 + T$	$1 - 2 T + 7 T^{2}$
2-269-1.1-c1-0-17	Elliptic curve 269.a Modular form 269.2.a.a Modular form 269.2.a.a.1.1	$1 + 2 T^{2}$	$1 + 3 T^{2}$	$1 - T + 5 T^{2}$	$1 + 4 T + 7 T^{2}$