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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 95 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
1856.1.h.a	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}-q^{11}+q^{13}-q^{15}+2q^{19}+\cdots$
1856.1.h.b	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-2q^{5}-q^{9}+2q^{13}+3q^{25}+q^{29}+\cdots$
1856.1.h.c	$1856$	$1$	1856.h	116.d	$2$	$1$	$1$	$0.926$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{11}+q^{13}+q^{15}-2q^{19}+\cdots$
1856.1.h.d	$1856$	$1$	1856.h	116.d	$2$	$2$	$2$	$0.926$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta q^{3}+q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots$
1856.1.l.a	$1856$	$1$	1856.l	29.c	$4$	$2$	$1$	$0.926$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{9}+iq^{13}+(1+i)q^{17}+q^{25}+\cdots$
1856.1.l.b	$1856$	$1$	1856.l	29.c	$4$	$4$	$2$	$0.926$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots$
1856.1.bd.a	$1856$	$1$	1856.bd	116.h	$14$	$6$	$1$	$0.926$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(\zeta_{14}+\zeta_{14}^{3})q^{5}-\zeta_{14}^{6}q^{9}+(\zeta_{14}^{4}+\cdots)q^{13}+\cdots$
1856.1.bh.a	$1856$	$1$	1856.bh	116.j	$14$	$6$	$1$	$0.926$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{14}^{4}-\zeta_{14}^{6})q^{5}-\zeta_{14}q^{9}+(-\zeta_{14}^{2}+\cdots)q^{13}+\cdots$
1856.1.ca.a	$1856$	$1$	1856.ca	29.f	$28$	$12$	$1$	$0.926$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{28}^{4}-\zeta_{28}^{12})q^{5}-\zeta_{28}^{3}q^{9}+(-\zeta_{28}^{9}+\cdots)q^{13}+\cdots$
1856.2.a.a	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}-4q^{7}+6q^{9}-q^{11}+\cdots$
1856.2.a.b	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{5}+2q^{7}+6q^{9}-q^{11}+\cdots$
1856.2.a.c	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots$
1856.2.a.d	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-1$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-4q^{7}-2q^{9}-3q^{11}+\cdots$
1856.2.a.e	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots$
1856.2.a.f	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots$
1856.2.a.g	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}+5q^{11}-q^{13}+\cdots$
1856.2.a.h	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{7}-2q^{9}-3q^{11}+\cdots$
1856.2.a.i	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+4q^{7}-2q^{9}+3q^{11}+\cdots$
1856.2.a.j	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}-2q^{9}+3q^{11}+\cdots$
1856.2.a.k	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}-2q^{9}+3q^{11}+\cdots$
1856.2.a.l	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots$
1856.2.a.m	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots$
1856.2.a.n	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots$
1856.2.a.o	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}+4q^{7}+6q^{9}+q^{11}+\cdots$
1856.2.a.p	$1856$	$2$	1856.a	1.a	$1$	$1$	$1$	$14.820$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+3q^{5}-2q^{7}+6q^{9}+q^{11}+\cdots$
1856.2.a.q	$1856$	$2$	1856.a	1.a	$1$	$2$	$2$	$14.820$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}+2q^{7}-2\beta q^{9}+\cdots$
1856.2.a.r	$1856$	$2$	1856.a	1.a	$1$	$2$	$2$	$14.820$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}-2\beta q^{9}+\cdots$
1856.2.a.s	$1856$	$2$	1856.a	1.a	$1$	$2$	$2$	$14.820$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1+2\beta )q^{5}+4q^{7}+\cdots$
1856.2.a.t	$1856$	$2$	1856.a	1.a	$1$	$2$	$2$	$14.820$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-3q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots$
1856.2.a.u	$1856$	$2$	1856.a	1.a	$1$	$2$	$2$	$14.820$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}-2q^{7}+2\beta q^{9}+(1+\cdots)q^{11}+\cdots$
1856.2.a.v	$1856$	$2$	1856.a	1.a	$1$	$2$	$2$	$14.820$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$2$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1-2\beta )q^{5}-4q^{7}+2\beta q^{9}+\cdots$
1856.2.a.w	$1856$	$2$	1856.a	1.a	$1$	$2$	$2$	$14.820$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+2\beta q^{7}+2\beta q^{9}+\cdots$
1856.2.a.x	$1856$	$2$	1856.a	1.a	$1$	$3$	$3$	$14.820$	3.3.568.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(2+\cdots)q^{9}+\cdots$
1856.2.a.y	$1856$	$2$	1856.a	1.a	$1$	$3$	$3$	$14.820$	3.3.568.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots$
1856.2.a.z	$1856$	$2$	1856.a	1.a	$1$	$4$	$4$	$14.820$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$8$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(2-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1856.2.a.ba	$1856$	$2$	1856.a	1.a	$1$	$5$	$5$	$14.820$	5.5.230224.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-4$	$2$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{4}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
1856.2.a.bb	$1856$	$2$	1856.a	1.a	$1$	$5$	$5$	$14.820$	5.5.230224.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$2$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{4}q^{5}+(-1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
1856.2.a.bc	$1856$	$2$	1856.a	1.a	$1$	$6$	$6$	$14.820$	6.6.68772992.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+(-1-\beta _{3})q^{5}-\beta _{1}q^{7}+(2+\cdots)q^{9}+\cdots$
1856.2.c.a	$1856$	$2$	1856.c	8.b	$2$	$8$	$8$	$14.820$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
1856.2.c.b	$1856$	$2$	1856.c	8.b	$2$	$8$	$8$	$14.820$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(-\beta _{3}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
1856.2.c.c	$1856$	$2$	1856.c	8.b	$2$	$20$	$20$	$14.820$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-16$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{13}q^{3}+\beta _{17}q^{5}+(-1+\beta _{8})q^{7}+\cdots$
1856.2.c.d	$1856$	$2$	1856.c	8.b	$2$	$20$	$20$	$14.820$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$16$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{13}q^{3}-\beta _{17}q^{5}+(1-\beta _{8})q^{7}+(-1+\cdots)q^{9}+\cdots$
1856.2.e.a	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-2$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-q^{5}-2q^{7}-4q^{9}-\beta q^{11}+\cdots$
1856.2.e.b	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-q^{5}-2q^{7}+2q^{9}-5iq^{11}+\cdots$
1856.2.e.c	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-2$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-q^{5}+2q^{7}-4q^{9}-\beta q^{11}+\cdots$
1856.2.e.d	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-q^{5}+2q^{7}+2q^{9}-5iq^{11}+\cdots$
1856.2.e.e	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{5}+3q^{9}+6q^{13}+4iq^{17}-q^{25}+\cdots$
1856.2.e.f	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+3q^{5}-2q^{7}-2q^{9}-\beta q^{11}+\cdots$
1856.2.e.g	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+3q^{5}+2q^{7}-2q^{9}-\beta q^{11}+\cdots$
1856.2.e.h	$1856$	$2$	1856.e	29.b	$2$	$4$	$4$	$14.820$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+2q^{9}+3\beta _{1}q^{11}+\cdots$

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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.