↑

Learn more

Refine 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
Sort order Select
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 at least 1000)

Next   To download results, determine the number of results.
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
2-26-1.1-c1-0-1 Elliptic curve 26.b Modular form 26.2.a.b Modular form 26.2.a.b.1.1 $1 - T$ $1 + 3 T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-61-1.1-c1-0-3 Elliptic curve 61.a Modular form 61.2.a.a Modular form 61.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
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 $1 - 2 T + 2 T^{2}$ $1 + 3 T^{2}$ $1 + T$ $1 - T + 7 T^{2}$
2-166-1.1-c1-0-5 Elliptic curve 166.a Modular form 166.2.a.a Modular form 166.2.a.a.1.1 $1 + T$ $1 + T + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-174-1.1-c1-0-3 Elliptic curve 174.d Modular form 174.2.a.d Modular form 174.2.a.d.1.1 $1 - T$ $1 + T$ $1 - T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-174-1.1-c1-0-4 Elliptic curve 174.e Modular form 174.2.a.e Modular form 174.2.a.e.1.1 $1 - T$ $1 - T$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$
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 $1 + T$ $1 + 3 T^{2}$ $1 - 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-208-1.1-c1-0-4 Elliptic curve 208.a Modular form 208.2.a.a Modular form 208.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-228-1.1-c1-0-3 Elliptic curve 228.a Modular form 228.2.a.a Modular form 228.2.a.a.1.1 $1$ $1 + T$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-234-1.1-c1-0-0 Elliptic curve 234.b Modular form 234.2.a.b Modular form 234.2.a.b.1.1 $1 + T$ $1$ $1 - T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-235-1.1-c1-0-2 Elliptic curve 235.a Modular form 235.2.a.a Modular form 235.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1 + T$ $1 - T + 7 T^{2}$
2-235-1.1-c1-0-8 Elliptic curve 235.b Modular form 235.2.a.b Modular form 235.2.a.b.1.1 $1 + T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1 - T$ $1 - T + 7 T^{2}$
2-258-1.1-c1-0-3 Elliptic curve 258.f Modular form 258.2.a.f Modular form 258.2.a.f.1.1 $1 - T$ $1 - T$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-286-1.1-c1-0-5 Elliptic curve 286.e Modular form 286.2.a.e Modular form 286.2.a.e.1.1 $1 - T$ $1 - 2 T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-286-1.1-c1-0-6 Elliptic curve 286.b Modular form 286.2.a.b Modular form 286.2.a.b.1.1 $1 + T$ $1 + T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-296-1.1-c1-0-7 Elliptic curve 296.a Modular form 296.2.a.a Modular form 296.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-297-1.1-c1-0-5 Elliptic curve 297.a Modular form 297.2.a.a Modular form 297.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1$ $1 + 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-297-1.1-c1-0-8 Elliptic curve 297.d Modular form 297.2.a.d Modular form 297.2.a.d.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-300-1.1-c1-0-0 Elliptic curve 300.b Modular form 300.2.a.b Modular form 300.2.a.b.1.1 $1$ $1 + T$ $1$ $1 - T + 7 T^{2}$
2-304-1.1-c1-0-1 Elliptic curve 304.c Modular form 304.2.a.c Modular form 304.2.a.c.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - T + 7 T^{2}$
2-304-1.1-c1-0-5 Elliptic curve 304.f Modular form 304.2.a.f Modular form 304.2.a.f.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-316-1.1-c1-0-3 Elliptic curve 316.a Modular form 316.2.a.a Modular form 316.2.a.a.1.1 $1$ $1 + 3 T + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-318-1.1-c1-0-1 Elliptic curve 318.b Modular form 318.2.a.b Modular form 318.2.a.b.1.1 $1 + T$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-318-1.1-c1-0-3 Elliptic curve 318.e Modular form 318.2.a.e Modular form 318.2.a.e.1.1 $1 - T$ $1 + T$ $1 + 5 T^{2}$ $1 - T + 7 T^{2}$
2-334-1.1-c1-0-7 Elliptic curve 334.a Modular form 334.2.a.a Modular form 334.2.a.a.1.1 $1 - T$ $1 + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-338-1.1-c1-0-9 Elliptic curve 338.f Modular form 338.2.a.f Modular form 338.2.a.f.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-339-1.1-c1-0-11 Elliptic curve 339.a Modular form 339.2.a.a Modular form 339.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-345-1.1-c1-0-0 Elliptic curve 345.c Modular form 345.2.a.c Modular form 345.2.a.c.1.1 $1 + 2 T^{2}$ $1 + T$ $1 + T$ $1 - T + 7 T^{2}$
2-348-1.1-c1-0-0 Elliptic curve 348.a Modular form 348.2.a.a Modular form 348.2.a.a.1.1 $1$ $1 + T$ $1 + 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-348-1.1-c1-0-1 Elliptic curve 348.d Modular form 348.2.a.d Modular form 348.2.a.d.1.1 $1$ $1 - T$ $1 - 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-359-1.1-c1-0-26 Elliptic curve 359.b Modular form 359.2.a.b Modular form 359.2.a.b.1.1 $1 - T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-363-1.1-c1-0-3 Elliptic curve 363.a Modular form 363.2.a.a Modular form 363.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-366-1.1-c1-0-6 Elliptic curve 366.g Modular form 366.2.a.g Modular form 366.2.a.g.1.1 $1 - T$ $1 - T$ $1 - T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-370-1.1-c1-0-3 Elliptic curve 370.c Modular form 370.2.a.c Modular form 370.2.a.c.1.1 $1 + T$ $1 - 2 T + 3 T^{2}$ $1 - T$ $1 - T + 7 T^{2}$
2-415-1.1-c1-0-14 Elliptic curve 415.a Modular form 415.2.a.a Modular form 415.2.a.a.1.1 $1 - T + 2 T^{2}$ $1 - 3 T + 3 T^{2}$ $1 - T$ $1 - T + 7 T^{2}$
2-418-1.1-c1-0-9 Elliptic curve 418.c Modular form 418.2.a.c Modular form 418.2.a.c.1.1 $1 - T$ $1 - 3 T + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-423-1.1-c1-0-12 Elliptic curve 423.g Modular form 423.2.a.g Modular form 423.2.a.g.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-423-1.1-c1-0-7 Elliptic curve 423.a Modular form 423.2.a.a Modular form 423.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-425-1.1-c1-0-22 Elliptic curve 425.c Modular form 425.2.a.c Modular form 425.2.a.c.1.1 $1 - T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1$ $1 - T + 7 T^{2}$
2-430-1.1-c1-0-9 Elliptic curve 430.a Modular form 430.2.a.a Modular form 430.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 + T$ $1 - T + 7 T^{2}$
2-432-1.1-c1-0-2 Elliptic curve 432.e Modular form 432.2.a.e Modular form 432.2.a.e.1.1 $1$ $1$ $1 + 5 T^{2}$ $1 - T + 7 T^{2}$
2-432-1.1-c1-0-3 Elliptic curve 432.g Modular form 432.2.a.g Modular form 432.2.a.g.1.1 $1$ $1$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-432-1.1-c1-0-5 Elliptic curve 432.b Modular form 432.2.a.b Modular form 432.2.a.b.1.1 $1$ $1$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-440-1.1-c1-0-7 Elliptic curve 440.d Modular form 440.2.a.d Modular form 440.2.a.d.1.1 $1$ $1 - 3 T + 3 T^{2}$ $1 - T$ $1 - T + 7 T^{2}$
2-443-1.1-c1-0-16 Elliptic curve 443.a Modular form 443.2.a.a Modular form 443.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - T + 7 T^{2}$
2-459-1.1-c1-0-17 Elliptic curve 459.h Modular form 459.2.a.h Modular form 459.2.a.h.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-459-1.1-c1-0-9 Elliptic curve 459.a Modular form 459.2.a.a Modular form 459.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1$ $1 + 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-467-1.1-c1-0-21 Elliptic curve 467.a Modular form 467.2.a.a Modular form 467.2.a.a.1.1 $1 + 2 T^{2}$ $1 + 3 T + 3 T^{2}$ $1 - 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-472-1.1-c1-0-11 Elliptic curve 472.b Modular form 472.2.a.b Modular form 472.2.a.b.1.1 $1$ $1 + T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-472-1.1-c1-0-2 Elliptic curve 472.c Modular form 472.2.a.c Modular form 472.2.a.c.1.1 $1$ $1 + T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$
Next