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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 87 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1734.2.a.a	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots$
1734.2.a.b	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
1734.2.a.c	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
1734.2.a.d	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots$
1734.2.a.e	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
1734.2.a.f	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
1734.2.a.g	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
1734.2.a.h	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+2q^{7}+\cdots$
1734.2.a.i	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots$
1734.2.a.j	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
1734.2.a.k	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+4q^{7}+\cdots$
1734.2.a.l	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots$
1734.2.a.m	$1734$	$2$	1734.a	1.a	$1$	$1$	$1$	$13.846$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+3q^{7}+\cdots$
1734.2.a.n	$1734$	$2$	1734.a	1.a	$1$	$2$	$2$	$13.846$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots$
1734.2.a.o	$1734$	$2$	1734.a	1.a	$1$	$2$	$2$	$13.846$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots$
1734.2.a.p	$1734$	$2$	1734.a	1.a	$1$	$3$	$3$	$13.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$-3$	$-6$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots$
1734.2.a.q	$1734$	$2$	1734.a	1.a	$1$	$3$	$3$	$13.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$3$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(2-\beta _{1})q^{5}-q^{6}+\cdots$
1734.2.a.r	$1734$	$2$	1734.a	1.a	$1$	$3$	$3$	$13.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$-3$	$-6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}-q^{6}+\cdots$
1734.2.a.s	$1734$	$2$	1734.a	1.a	$1$	$3$	$3$	$13.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$3$	$6$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(2-\beta _{1})q^{5}+q^{6}+\cdots$
1734.2.a.t	$1734$	$2$	1734.a	1.a	$1$	$4$	$4$	$13.846$	$\Q(\zeta_{16})^+$	None	✓	$1$	$0$	$-4$	$-4$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(2+\beta _{2}+\beta _{3})q^{5}+\cdots$
1734.2.a.u	$1734$	$2$	1734.a	1.a	$1$	$4$	$4$	$13.846$	$\Q(\zeta_{16})^+$	None	✓	$1$	$1$	$-4$	$4$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2-\beta _{2}+\beta _{3})q^{5}+\cdots$
1734.2.a.v	$1734$	$2$	1734.a	1.a	$1$	$4$	$4$	$13.846$	$\Q(\zeta_{16})^+$	None	✓	$1$	$1$	$4$	$-4$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots$
1734.2.a.w	$1734$	$2$	1734.a	1.a	$1$	$4$	$4$	$13.846$	$\Q(\zeta_{16})^+$	None	✓	$1$	$0$	$4$	$4$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+q^{6}+\cdots$
1734.2.b.a	$1734$	$2$	1734.b	17.b	$2$	$2$	$2$	$13.846$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+iq^{3}+q^{4}+4iq^{5}-iq^{6}+\cdots$
1734.2.b.b	$1734$	$2$	1734.b	17.b	$2$	$2$	$2$	$13.846$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-iq^{3}+q^{4}+2iq^{5}+iq^{6}+\cdots$
1734.2.b.c	$1734$	$2$	1734.b	17.b	$2$	$2$	$2$	$13.846$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-iq^{3}+q^{4}+3iq^{5}+iq^{6}+\cdots$
1734.2.b.d	$1734$	$2$	1734.b	17.b	$2$	$2$	$2$	$13.846$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}+q^{4}+4iq^{5}+iq^{6}+\cdots$
1734.2.b.e	$1734$	$2$	1734.b	17.b	$2$	$2$	$2$	$13.846$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}+q^{4}+iq^{6}+iq^{7}+q^{8}+\cdots$
1734.2.b.f	$1734$	$2$	1734.b	17.b	$2$	$2$	$2$	$13.846$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-iq^{3}+q^{4}-iq^{6}+2iq^{7}+\cdots$
1734.2.b.g	$1734$	$2$	1734.b	17.b	$2$	$2$	$2$	$13.846$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}+q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots$
1734.2.b.h	$1734$	$2$	1734.b	17.b	$2$	$4$	$4$	$13.846$	$\Q(\zeta_{8})$	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\zeta_{8}q^{3}+q^{4}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots$
1734.2.b.i	$1734$	$2$	1734.b	17.b	$2$	$6$	$6$	$13.846$	6.0.419904.1	None		$2$	$0$	$-6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots$
1734.2.b.j	$1734$	$2$	1734.b	17.b	$2$	$6$	$6$	$13.846$	6.0.419904.1	None		$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots$
1734.2.b.k	$1734$	$2$	1734.b	17.b	$2$	$8$	$8$	$13.846$	$\Q(\zeta_{16})$	None		$2$	$0$	$-8$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\zeta_{16}q^{3}+q^{4}+(\zeta_{16}^{2}+\zeta_{16}^{3}+\cdots)q^{5}+\cdots$
1734.2.b.l	$1734$	$2$	1734.b	17.b	$2$	$8$	$8$	$13.846$	$\Q(\zeta_{16})$	None		$2$	$0$	$8$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\zeta_{16}q^{3}+q^{4}+(2\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{5}+\cdots$
1734.2.f.a	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots$
1734.2.f.b	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\zeta_{8}q^{6}+\cdots$
1734.2.f.c	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+3\zeta_{8}q^{5}+\cdots$
1734.2.f.d	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}-\zeta_{8}q^{6}+\cdots$
1734.2.f.e	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+2\zeta_{8}q^{5}+\cdots$
1734.2.f.f	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+4\zeta_{8}q^{5}+\cdots$
1734.2.f.g	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+4\zeta_{8}q^{5}+\cdots$
1734.2.f.h	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+2\zeta_{8}q^{5}+\cdots$
1734.2.f.i	$1734$	$2$	1734.f	17.c	$4$	$4$	$2$	$13.846$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots$
1734.2.f.j	$1734$	$2$	1734.f	17.c	$4$	$8$	$4$	$13.846$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$-8$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{5}q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$
1734.2.f.k	$1734$	$2$	1734.f	17.c	$4$	$8$	$4$	$13.846$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$-8$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{16}^{3}q^{2}+\zeta_{16}q^{3}-q^{4}+(-1+2\zeta_{16}+\cdots)q^{5}+\cdots$
1734.2.f.l	$1734$	$2$	1734.f	17.c	$4$	$8$	$4$	$13.846$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$8$	$-8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{16}^{3}q^{2}+\zeta_{16}q^{3}-q^{4}+(1+2\zeta_{16}+\cdots)q^{5}+\cdots$
1734.2.f.m	$1734$	$2$	1734.f	17.c	$4$	$8$	$4$	$13.846$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$8$	$-8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{16}^{3}q^{2}-\zeta_{16}q^{3}-q^{4}+(1+\zeta_{16}^{3}+\cdots)q^{5}+\cdots$
1734.2.f.n	$1734$	$2$	1734.f	17.c	$4$	$12$	$6$	$13.846$	12.0.$\cdots$.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{2}-\beta _{10}q^{3}-q^{4}+(2\beta _{10}-\beta _{11})q^{5}+\cdots$
1734.2.f.o	$1734$	$2$	1734.f	17.c	$4$	$12$	$6$	$13.846$	12.0.$\cdots$.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}-\beta _{10}q^{3}-q^{4}+(2\beta _{10}-\beta _{11})q^{5}+\cdots$

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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.