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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 184 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2448.1.i.a	$2448$	$1$	2448.i	68.d	$2$	$2$	$2$	$1.222$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{7}-\beta q^{11}+q^{17}+\beta q^{23}+q^{25}+\cdots$
2448.1.i.b	$2448$	$1$	2448.i	68.d	$2$	$2$	$2$	$1.222$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-51}) $	$\Q(\sqrt{51}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{5}+q^{13}-iq^{17}-3q^{25}+iq^{29}+\cdots$
2448.1.i.c	$2448$	$1$	2448.i	68.d	$2$	$4$	$4$	$1.222$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q-\zeta_{12}^{3}q^{5}+(-\zeta_{12}+\zeta_{12}^{5})q^{11}+\cdots$
2448.1.m.a	$2448$	$1$	2448.m	51.c	$2$	$2$	$2$	$1.222$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}-\beta q^{7}+q^{11}-q^{13}-q^{17}+\cdots$
2448.1.m.b	$2448$	$1$	2448.m	51.c	$2$	$2$	$2$	$1.222$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-\beta q^{7}-q^{11}-q^{13}+q^{17}+\cdots$
2448.1.w.a	$2448$	$1$	2448.w	272.k	$4$	$2$	$1$	$1.222$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}+(-1-i)q^{13}+\cdots$
2448.1.w.b	$2448$	$1$	2448.w	272.k	$4$	$2$	$1$	$1.222$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-q^{4}-iq^{8}+(-1-i)q^{13}+\cdots$
2448.1.bd.a	$2448$	$1$	2448.bd	51.f	$4$	$4$	$2$	$1.222$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{5}+\zeta_{8}q^{11}+q^{13}-\zeta_{8}q^{17}+\cdots$
2448.1.bf.a	$2448$	$1$	2448.bf	68.f	$4$	$2$	$1$	$1.222$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-1-i)q^{5}-iq^{17}+iq^{25}+(-1+\cdots)q^{29}+\cdots$
2448.1.bf.b	$2448$	$1$	2448.bf	68.f	$4$	$2$	$1$	$1.222$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(1+i)q^{5}+iq^{17}+iq^{25}+(1+i+\cdots)q^{29}+\cdots$
2448.1.bw.a	$2448$	$1$	2448.bw	612.q	$6$	$8$	$4$	$1.222$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{3}+(-\zeta_{24}-\zeta_{24}^{7})q^{7}+\zeta_{24}^{10}q^{9}+\cdots$
2448.1.cf.a	$2448$	$1$	2448.cf	68.g	$8$	$4$	$1$	$1.222$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}+\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{13}-\zeta_{8}^{2}q^{17}+\cdots$
2448.1.de.a	$2448$	$1$	2448.de	612.aa	$12$	$8$	$2$	$1.222$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{9}+\zeta_{24}^{11}q^{11}+\cdots$
2448.1.ed.a	$2448$	$1$	2448.ed	204.t	$16$	$8$	$1$	$1.222$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-8$	$0$		$1$		$q+(-1-\zeta_{16}^{7})q^{5}+(\zeta_{16}-\zeta_{16}^{3})q^{13}+\cdots$
2448.1.ed.b	$2448$	$1$	2448.ed	204.t	$16$	$8$	$1$	$1.222$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$8$	$0$		$1$		$q+(1+\zeta_{16}^{7})q^{5}+(\zeta_{16}-\zeta_{16}^{3})q^{13}+\cdots$
2448.2.a.a	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-2q^{7}+3q^{11}-q^{13}+q^{17}+\cdots$
2448.2.a.b	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-q^{11}+3q^{13}+q^{17}-q^{19}+\cdots$
2448.2.a.c	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}-3q^{11}-q^{13}+q^{17}+\cdots$
2448.2.a.d	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}+4q^{11}+6q^{13}-q^{17}+\cdots$
2448.2.a.e	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+5q^{11}-5q^{13}-q^{17}-q^{19}+\cdots$
2448.2.a.f	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{11}-q^{13}-q^{17}+\cdots$
2448.2.a.g	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+3q^{11}-5q^{13}-q^{17}+\cdots$
2448.2.a.h	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{13}+q^{17}-4q^{19}+2q^{23}+\cdots$
2448.2.a.i	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{13}+q^{17}+4q^{19}-6q^{23}+\cdots$
2448.2.a.j	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{11}-6q^{13}+q^{17}-4q^{19}+4q^{23}+\cdots$
2448.2.a.k	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}+6q^{11}+2q^{13}+q^{17}+4q^{19}+\cdots$
2448.2.a.l	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+3q^{11}+3q^{13}+q^{17}+\cdots$
2448.2.a.m	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{11}-5q^{13}+q^{17}+\cdots$
2448.2.a.n	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+3q^{11}-q^{13}+q^{17}+\cdots$
2448.2.a.o	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-2q^{13}-q^{17}+4q^{19}+\cdots$
2448.2.a.p	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{11}-2q^{13}-q^{17}-4q^{19}+\cdots$
2448.2.a.q	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-6q^{11}+2q^{13}-q^{17}+\cdots$
2448.2.a.r	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{7}-3q^{11}-q^{13}-q^{17}+\cdots$
2448.2.a.s	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}+q^{11}-5q^{13}-q^{17}+\cdots$
2448.2.a.t	$2448$	$2$	2448.a	1.a	$1$	$1$	$1$	$19.547$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}-6q^{13}+q^{17}-4q^{19}+\cdots$
2448.2.a.u	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+\cdots$
2448.2.a.v	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(-1+\beta )q^{11}+(3-\beta )q^{13}+\cdots$
2448.2.a.w	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2+\beta )q^{7}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots$
2448.2.a.x	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2-\beta )q^{7}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots$
2448.2.a.y	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+(1+\beta )q^{7}+(-3+\beta )q^{11}+\cdots$
2448.2.a.z	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-4q^{7}+(-2+\beta )q^{11}+\beta q^{13}+\cdots$
2448.2.a.ba	$2448$	$2$	2448.a	1.a	$1$	$2$	$2$	$19.547$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(2-2\beta )q^{7}+(-4-\beta )q^{11}+\cdots$
2448.2.a.bb	$2448$	$2$	2448.a	1.a	$1$	$3$	$3$	$19.547$	3.3.1304.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots$
2448.2.a.bc	$2448$	$2$	2448.a	1.a	$1$	$3$	$3$	$19.547$	3.3.1304.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots$
2448.2.c.a	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}-iq^{7}-6q^{13}+(1+2i)q^{17}+\cdots$
2448.2.c.b	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{5}+4iq^{7}-iq^{11}-5q^{13}+\cdots$
2448.2.c.c	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{5}-4iq^{7}-iq^{11}-5q^{13}+\cdots$
2448.2.c.d	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}-3\beta q^{7}+\beta q^{11}-4q^{13}+\cdots$
2448.2.c.e	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{7}-iq^{11}-2q^{13}+(-1-2i)q^{17}+\cdots$
2448.2.c.f	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{5}+2iq^{7}+5iq^{11}-q^{13}+\cdots$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.