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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 338 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
450.2.a.a	$450$	$2$	450.a	1.a	$1$	$1$	$1$	$3.593$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-6q^{11}+4q^{13}+\cdots$
450.2.a.b	$450$	$2$	450.a	1.a	$1$	$1$	$1$	$3.593$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots$
450.2.a.c	$450$	$2$	450.a	1.a	$1$	$1$	$1$	$3.593$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+3q^{11}+4q^{13}+\cdots$
450.2.a.d	$450$	$2$	450.a	1.a	$1$	$1$	$1$	$3.593$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-2q^{13}-4q^{14}+\cdots$
450.2.a.e	$450$	$2$	450.a	1.a	$1$	$1$	$1$	$3.593$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+6q^{11}+4q^{13}+\cdots$
450.2.a.f	$450$	$2$	450.a	1.a	$1$	$1$	$1$	$3.593$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots$
450.2.a.g	$450$	$2$	450.a	1.a	$1$	$1$	$1$	$3.593$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots$
450.2.c.a	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-6q^{11}+\cdots$
450.2.c.b	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-4iq^{7}-iq^{8}-2iq^{13}+\cdots$
450.2.c.c	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{11}+\cdots$
450.2.c.d	$450$	$2$	450.c	5.b	$2$	$2$	$2$	$3.593$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-2iq^{7}-iq^{8}+6q^{11}+\cdots$
450.2.e.a	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$-3$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.b	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.c	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.d	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$3$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.e	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-3$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.f	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.g	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$3$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.h	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$3$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.i	$450$	$2$	450.e	9.c	$3$	$2$	$1$	$3.593$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$3$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
450.2.e.j	$450$	$2$	450.e	9.c	$3$	$4$	$2$	$3.593$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$-2$	$-2$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
450.2.e.k	$450$	$2$	450.e	9.c	$3$	$4$	$2$	$3.593$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$-2$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
450.2.e.l	$450$	$2$	450.e	9.c	$3$	$4$	$2$	$3.593$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$-2$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
450.2.e.m	$450$	$2$	450.e	9.c	$3$	$4$	$2$	$3.593$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$2$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}+(-1+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
450.2.e.n	$450$	$2$	450.e	9.c	$3$	$4$	$2$	$3.593$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$2$	$-2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
450.2.f.a	$450$	$2$	450.f	15.e	$4$	$4$	$2$	$3.593$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-3+3\zeta_{8}^{2})q^{7}+\cdots$
450.2.f.b	$450$	$2$	450.f	15.e	$4$	$4$	$2$	$3.593$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+2\zeta_{8}^{2})q^{7}+\cdots$
450.2.f.c	$450$	$2$	450.f	15.e	$4$	$4$	$2$	$3.593$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(3-3\zeta_{8}^{2})q^{7}+\cdots$
450.2.h.a	$450$	$2$	450.h	25.d	$5$	$4$	$1$	$3.593$	$\Q(\zeta_{10})$	None		$2$	$1$	$-1$	$0$	$-5$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
450.2.h.b	$450$	$2$	450.h	25.d	$5$	$4$	$1$	$3.593$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$0$	$-5$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
450.2.h.c	$450$	$2$	450.h	25.d	$5$	$4$	$1$	$3.593$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$0$	$-5$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots$
450.2.h.d	$450$	$2$	450.h	25.d	$5$	$8$	$2$	$3.593$	8.0.1064390625.3	None		$2$	$0$	$-2$	$0$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{4}+\cdots$
450.2.h.e	$450$	$2$	450.h	25.d	$5$	$8$	$2$	$3.593$	8.0.58140625.2	None		$2$	$0$	$2$	$0$	$0$	$4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}-\beta _{3}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
450.2.h.f	$450$	$2$	450.h	25.d	$5$	$12$	$3$	$3.593$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-3$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots$
450.2.h.g	$450$	$2$	450.h	25.d	$5$	$12$	$3$	$3.593$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots$
450.2.j.a	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
450.2.j.b	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
450.2.j.c	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
450.2.j.d	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
450.2.j.e	$450$	$2$	450.j	45.j	$6$	$4$	$2$	$3.593$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
450.2.j.f	$450$	$2$	450.j	45.j	$6$	$8$	$4$	$3.593$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots$
450.2.j.g	$450$	$2$	450.j	45.j	$6$	$8$	$4$	$3.593$	8.0.303595776.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3}-\beta _{5}-\beta _{7})q^{3}+\cdots$
450.2.l.a	$450$	$2$	450.l	25.e	$10$	$8$	$2$	$3.593$	$\Q(\zeta_{20})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{5}+\cdots$
450.2.l.b	$450$	$2$	450.l	25.e	$10$	$8$	$2$	$3.593$	$\Q(\zeta_{20})$	None		$2$	$0$	$0$	$0$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(1-\zeta_{20}-\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
450.2.l.c	$450$	$2$	450.l	25.e	$10$	$16$	$4$	$3.593$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$5$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{8}q^{2}-\beta _{10}q^{4}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$
450.2.l.d	$450$	$2$	450.l	25.e	$10$	$16$	$4$	$3.593$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{11}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots$
450.2.p.a	$450$	$2$	450.p	45.l	$12$	$8$	$2$	$3.593$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$-4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}+(-1-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots$
450.2.p.b	$450$	$2$	450.p	45.l	$12$	$8$	$2$	$3.593$	$\Q(\zeta_{24})$	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}-\zeta_{24}^{5})q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
450.2.p.c	$450$	$2$	450.p	45.l	$12$	$8$	$2$	$3.593$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}+(\zeta_{24}^{3}-2\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
450.2.p.d	$450$	$2$	450.p	45.l	$12$	$8$	$2$	$3.593$	$\Q(\zeta_{24})$	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}+(-2\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots$

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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.