↑

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 162 matches)

Next   displayed columns for results
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-16928-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-1058.1-a Elliptic curve 2.0.4.1-1058.1-a $1 + T$ $( 1 + 3 T^{2} )^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-168e2-1.1-c1e2-0-19 Bianchi modular form 2.0.4.1-1764.1-b Elliptic curve 2.0.4.1-1764.1-b $1$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + T )$
4-2e16-1.1-c1e2-0-9 Elliptic curve 2.0.4.1-4096.1-CMc $1$ $( 1 + 3 T^{2} )^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-288e2-1.1-c1e2-0-17 Elliptic curve 2.0.4.1-5184.1-CMc $1$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-93312-1.1-c1e2-0-27 Bianchi modular form 2.0.4.1-5832.1-d Elliptic curve 2.0.4.1-5832.1-d $1$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-107811-1.1-c1e2-0-3 Bianchi modular form 2.0.11.1-891.3-c Elliptic curve 2.0.11.1-891.3-c $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-348e2-1.1-c1e2-0-4 Elliptic curve 2.2.29.1-144.1-a Hilbert modular form 2.2.29.1-144.1-a Modular form 348.2.h.c $1$ $1 + T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )^{2}$
4-363e2-1.1-c1e2-0-7 Bianchi modular form 2.0.11.1-1089.2-b Elliptic curve 2.0.11.1-1089.2-b $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 + T )^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-139392-1.1-c1e2-0-30 Bianchi modular form 2.0.4.1-8712.1-d Elliptic curve 2.0.4.1-8712.1-d $1$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-384e2-1.1-c1e2-0-35 Bianchi modular form 2.0.4.1-9216.1-l Elliptic curve 2.0.4.1-9216.1-l $1$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-148176-1.1-c1e2-0-7 Elliptic curve 2.2.21.1-336.1-b Hilbert modular form 2.2.21.1-336.1-b $1$ $1 + T$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 + T$
4-396e2-1.1-c1e2-0-23 Bianchi modular form 2.0.4.1-9801.1-c Elliptic curve 2.0.4.1-9801.1-c $1 - T + 2 T^{2}$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-156996-1.1-c1e2-0-6 Elliptic curve 2.2.21.1-356.1-a Elliptic curve 2.2.21.1-356.2-a Hilbert modular form 2.2.21.1-356.1-a Hilbert modular form 2.2.21.1-356.2-a $( 1 - T )( 1 + T )$ $1 - T + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 + 2 T + 7 T^{2}$
4-165888-1.1-c1e2-0-27 Elliptic curve 2.2.24.1-288.1-e Hilbert modular form 2.2.24.1-288.1-e $1$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-56e3-1.1-c1e2-0-16 Elliptic curve 2.2.56.1-56.1-a Hilbert modular form 2.2.56.1-56.1-a $1$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 + T$
4-178432-1.1-c1e2-0-13 Bianchi modular form 2.0.4.1-11152.2-b Bianchi modular form 2.0.4.1-11152.3-b Elliptic curve 2.0.4.1-11152.2-b Elliptic curve 2.0.4.1-11152.3-b $1$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 + 6 T^{2} + 49 T^{4}$
4-436e2-1.1-c1e2-0-2 Elliptic curve 2.0.4.1-11881.1-CMa Elliptic curve 2.0.4.1-11881.3-CMa Modular form 436.2.f.a $1 + 2 T + 2 T^{2}$ $( 1 - 3 T^{2} )^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 7 T^{2} )^{2}$
4-194688-1.1-c1e2-0-23 Bianchi modular form 2.0.4.1-12168.2-f Elliptic curve 2.0.4.1-12168.2-f $1$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-442e2-1.1-c1e2-0-40 Modular form 442.2.e.a $1 + T + T^{2}$ $1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-197568-1.1-c1e2-0-26 Elliptic curve 2.2.21.1-448.1-a Hilbert modular form 2.2.21.1-448.1-a $1$ $1 + 2 T + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 - T$
4-448e2-1.1-c1e2-0-22 Bianchi modular form 2.0.4.1-12544.1-f Elliptic curve 2.0.4.1-12544.1-f $1$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + T )$
4-225792-1.1-c1e2-0-50 Elliptic curve 2.2.24.1-392.1-a Hilbert modular form 2.2.24.1-392.1-a $1$ $1 - 2 T + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + T )$
4-233409-1.1-c1e2-0-1 Bianchi modular form 2.0.11.1-1929.2-a Bianchi modular form 2.0.11.1-1929.3-a Elliptic curve 2.0.11.1-1929.2-a Elliptic curve 2.0.11.1-1929.3-a $1 - 2 T^{2} + 4 T^{4}$ $( 1 - T )( 1 + T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 - 5 T^{2} + 49 T^{4}$
4-243072-1.1-c1e2-0-7 Elliptic curve 2.2.24.1-422.1-b Elliptic curve 2.2.24.1-422.2-b Hilbert modular form 2.2.24.1-422.1-b Hilbert modular form 2.2.24.1-422.2-b $1 - T$ $1 - T + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 + 2 T^{2} + 49 T^{4}$
4-506e2-1.1-c1e2-0-1 Bianchi modular form 2.0.11.1-2116.2-b Elliptic curve 2.0.11.1-2116.2-b $( 1 - T )( 1 + T )$ $( 1 + 3 T^{2} )^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-259308-1.1-c1e2-0-12 Elliptic curve 2.2.21.1-588.1-a Hilbert modular form 2.2.21.1-588.1-a $( 1 - T )( 1 + T )$ $1 + T$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1$
4-264992-1.1-c1e2-0-12 Bianchi modular form 2.0.4.1-16562.2-b Elliptic curve 2.0.4.1-16562.2-b $1 + T$ $( 1 - T + 3 T^{2} )( 1 + T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + T )$
4-528e2-1.1-c1e2-0-67 Bianchi modular form 2.0.11.1-2304.2-g Bianchi modular form 2.0.11.1-2304.2-l Elliptic curve 2.0.11.1-2304.2-g Elliptic curve 2.0.11.1-2304.2-l Elliptic curve 2.2.44.1-144.1-h Elliptic curve 2.2.44.1-144.1-l Hilbert modular form 2.2.44.1-144.1-h Hilbert modular form 2.2.44.1-144.1-l $1$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-544e2-1.1-c1e2-0-23 Bianchi modular form 2.0.4.1-18496.2-e Elliptic curve 2.0.4.1-18496.2-e $1$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-546e2-1.1-c1e2-0-62 Modular form 546.2.l.h $1 - T + T^{2}$ $1 - T + T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 + T + T^{2}$
4-301088-1.1-c1e2-0-4 Bianchi modular form 2.0.4.1-18818.2-a Elliptic curve 2.0.4.1-18818.2-a $1 - T$ $( 1 + 3 T^{2} )^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-552e2-1.1-c1e2-0-4 Elliptic curve 2.2.24.1-529.1-a Hilbert modular form 2.2.24.1-529.1-a Modular form 552.2.j.b $1 + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 - 6 T^{2} + 49 T^{4}$
4-307328-1.1-c1e2-0-24 Bianchi modular form 2.0.4.1-19208.1-f Elliptic curve 2.0.4.1-19208.1-f $1$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1$
4-313632-1.1-c1e2-0-49 Bianchi modular form 2.0.4.1-19602.1-c Elliptic curve 2.0.4.1-19602.1-c $1 + T$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-567e2-1.1-c1e2-0-35 Modular form 567.2.g.e $1 - T - T^{2} - 2 T^{3} + 4 T^{4}$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 - T + 7 T^{2}$
4-24e4-1.1-c1e2-0-52 Elliptic curve 2.0.4.1-20736.1-CMa $1$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-338688-1.1-c1e2-0-43 Elliptic curve 2.2.24.1-588.1-c Hilbert modular form 2.2.24.1-588.1-c $1$ $1 + T$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T )( 1 + T )$
4-339488-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-21218.1-a Elliptic curve 2.0.4.1-21218.1-a $1 + T$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-351232-1.1-c1e2-0-16 Elliptic curve 2.2.56.1-112.1-c Hilbert modular form 2.2.56.1-112.1-c $1$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $1 - T$
4-596e2-1.1-c1e2-0-0 Elliptic curve 2.0.4.1-22201.1-CMa Elliptic curve 2.0.4.1-22201.3-CMa Modular form 596.2.f.a $1 + 2 T + 2 T^{2}$ $1 + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 + 7 T^{2} )^{2}$
4-603e2-1.1-c1e2-0-8 Modular form 603.2.g.b $1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4}$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-72e3-1.1-c1e2-0-15 Elliptic curve 2.2.24.1-648.1-e Hilbert modular form 2.2.24.1-648.1-e $1$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-384659-1.1-c1e2-0-0 Bianchi modular form 2.0.11.1-3179.1-a Elliptic curve 2.0.11.1-3179.1-a $( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $( 1 + 3 T^{2} )^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-393472-1.1-c1e2-0-1 Bianchi modular form 2.0.4.1-24592.2-b Bianchi modular form 2.0.4.1-24592.3-b Elliptic curve 2.0.4.1-24592.2-b Elliptic curve 2.0.4.1-24592.3-b $1$ $1 - 4 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-394272-1.1-c1e2-0-5 Bianchi modular form 2.0.4.1-24642.2-c Elliptic curve 2.0.4.1-24642.2-c $1 + T$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-415872-1.1-c1e2-0-19 Elliptic curve 2.2.24.1-722.1-d Hilbert modular form 2.2.24.1-722.1-d $1 + T$ $1 + T + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-415872-1.1-c1e2-0-38 Bianchi modular form 2.0.4.1-25992.1-f Elliptic curve 2.0.4.1-25992.1-f $1$ $( 1 - T )( 1 + T )$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-418176-1.1-c1e2-0-82 Elliptic curve 2.2.24.1-726.1-e Hilbert modular form 2.2.24.1-726.1-e $1 + T$ $1 - T$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-431244-1.1-c1e2-0-15 Bianchi modular form 2.0.11.1-3564.3-e Elliptic curve 2.0.11.1-3564.3-e $( 1 - T )( 1 + T )$ $1$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-438012-1.1-c1e2-0-1 Elliptic curve 2.2.69.1-92.1-a Hilbert modular form 2.2.69.1-92.1-a $( 1 - T )( 1 + T )$ $1 + 3 T^{2}$ $( 1 - 4 T + 5 T^{2} )^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
Next