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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 113 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
369.2.a.a	$369$	$2$	369.a	1.a	$1$	$1$	$1$	$2.946$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{5}-4q^{7}-5q^{11}-4q^{13}+\cdots$
369.2.a.b	$369$	$2$	369.a	1.a	$1$	$1$	$1$	$2.946$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+4q^{5}-2q^{7}+8q^{10}+\cdots$
369.2.a.c	$369$	$2$	369.a	1.a	$1$	$2$	$2$	$2.946$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-2-\beta )q^{5}+(-2-\beta )q^{7}+\cdots$
369.2.a.d	$369$	$2$	369.a	1.a	$1$	$3$	$3$	$2.946$	3.3.148.1	None	✓	$1$	$1$	$-2$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
369.2.a.e	$369$	$2$	369.a	1.a	$1$	$3$	$3$	$2.946$	3.3.316.1	None	✓	$1$	$0$	$-1$	$0$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
369.2.a.f	$369$	$2$	369.a	1.a	$1$	$3$	$3$	$2.946$	3.3.148.1	None	✓	$1$	$0$	$1$	$0$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+(1+2\beta _{1})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
369.2.a.g	$369$	$2$	369.a	1.a	$1$	$3$	$3$	$2.946$	3.3.148.1	None	✓	$1$	$0$	$2$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
369.2.d.a	$369$	$2$	369.d	41.b	$2$	$2$	$2$	$2.946$	$\Q(\sqrt{-5}) $	None		$2$	$1$	$-4$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{2}+2q^{4}-2q^{5}+2\beta q^{7}+4q^{10}+\cdots$
369.2.d.b	$369$	$2$	369.d	41.b	$2$	$2$	$2$	$2.946$	$\Q(\sqrt{-41}) $	$\Q(\sqrt{-123}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta q^{11}+4q^{16}+\beta q^{17}-5q^{25}+\cdots$
369.2.d.c	$369$	$2$	369.d	41.b	$2$	$2$	$2$	$2.946$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$2$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{4}-2q^{5}+\beta q^{7}-3q^{8}-2q^{10}+\cdots$
369.2.d.d	$369$	$2$	369.d	41.b	$2$	$2$	$2$	$2.946$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$4$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}+2q^{4}+2q^{5}+2\beta q^{7}+4q^{10}+\cdots$
369.2.d.e	$369$	$2$	369.d	41.b	$2$	$8$	$8$	$2.946$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$-2$	$0$	$8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{6})q^{5}+\cdots$
369.2.e.a	$369$	$2$	369.e	9.c	$3$	$32$	$16$	$2.946$		None		$2$	$0$	$0$	$-1$	$1$	$13$			$\mathrm{SU}(2)[C_{3}]$
369.2.e.b	$369$	$2$	369.e	9.c	$3$	$48$	$24$	$2.946$		None		$2$	$0$	$0$	$-1$	$1$	$-15$			$\mathrm{SU}(2)[C_{3}]$
369.2.f.a	$369$	$2$	369.f	41.c	$4$	$2$	$1$	$2.946$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+q^{4}+(-2+2i)q^{7}+3iq^{8}+\cdots$
369.2.f.b	$369$	$2$	369.f	41.c	$4$	$2$	$1$	$2.946$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-iq^{2}+q^{4}+(-2+2i)q^{7}-3iq^{8}+\cdots$
369.2.f.c	$369$	$2$	369.f	41.c	$4$	$6$	$3$	$2.946$	6.0.5089536.1	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{2}+(-1-\beta _{1}+\beta _{3})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
369.2.f.d	$369$	$2$	369.f	41.c	$4$	$12$	$6$	$2.946$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{10}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots$
369.2.f.e	$369$	$2$	369.f	41.c	$4$	$12$	$6$	$2.946$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-1+\beta _{5}-\beta _{7}+\beta _{10}+\beta _{11})q^{4}+\cdots$
369.2.h.a	$369$	$2$	369.h	41.d	$5$	$4$	$1$	$2.946$	$\Q(\zeta_{10})$	None		$2$	$0$	$5$	$0$	$8$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{3}q^{4}+\cdots$
369.2.h.b	$369$	$2$	369.h	41.d	$5$	$8$	$2$	$2.946$	8.0.13140625.1	None		$2$	$0$	$1$	$0$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+\beta _{7})q^{2}+(-2\beta _{1}-\beta _{2}+2\beta _{5}+\cdots)q^{4}+\cdots$
369.2.h.c	$369$	$2$	369.h	41.d	$5$	$12$	$3$	$2.946$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-4$	$0$	$-1$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
369.2.h.d	$369$	$2$	369.h	41.d	$5$	$16$	$4$	$2.946$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$1$	$0$	$1$	$-2$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{12}q^{2}+(-1+\beta _{1}+\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$
369.2.h.e	$369$	$2$	369.h	41.d	$5$	$24$	$6$	$2.946$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{5}]$
369.2.i.a	$369$	$2$	369.i	369.i	$6$	$80$	$40$	$2.946$		None		$4$	$0$	$-4$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
369.2.m.a	$369$	$2$	369.m	123.i	$8$	$28$	$7$	$2.946$		None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$
369.2.m.b	$369$	$2$	369.m	123.i	$8$	$28$	$7$	$2.946$		None		$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{8}]$
369.2.n.a	$369$	$2$	369.n	41.f	$10$	$4$	$1$	$2.946$	$\Q(\zeta_{10})$	None		$2$	$1$	$-3$	$0$	$-3$	$-10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\zeta_{10})q^{2}+(1+\zeta_{10}^{2})q^{4}-3\zeta_{10}q^{5}+\cdots$
369.2.n.b	$369$	$2$	369.n	41.f	$10$	$4$	$1$	$2.946$	$\Q(\zeta_{10})$	None		$2$	$0$	$3$	$0$	$3$	$-10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\zeta_{10})q^{2}+(1+\zeta_{10}^{2})q^{4}+3\zeta_{10}q^{5}+\cdots$
369.2.n.c	$369$	$2$	369.n	41.f	$10$	$8$	$2$	$2.946$	$\Q(\zeta_{15})$	None		$2$	$0$	$3$	$0$	$9$	$-5$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\zeta_{15}^{2}+\zeta_{15}^{5})q^{2}+(\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{4}+\cdots$
369.2.n.d	$369$	$2$	369.n	41.f	$10$	$16$	$4$	$2.946$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$20$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{12}q^{2}+(-\beta _{2}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$
369.2.n.e	$369$	$2$	369.n	41.f	$10$	$32$	$8$	$2.946$		None		$2$	$0$	$2$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{10}]$
369.2.r.a	$369$	$2$	369.r	369.r	$12$	$4$	$1$	$2.946$	$\Q(\zeta_{12})$	None		$2$	$1$	$-6$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-2+\zeta_{12}^{2})q^{2}+(1-2\zeta_{12}^{2})q^{3}+\cdots$
369.2.r.b	$369$	$2$	369.r	369.r	$12$	$4$	$1$	$2.946$	$\Q(\zeta_{12})$	None		$2$	$0$	$6$	$0$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(2-\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
369.2.r.c	$369$	$2$	369.r	369.r	$12$	$152$	$38$	$2.946$		None		$4$	$0$	$0$	$-2$	$0$	$4$			$\mathrm{SU}(2)[C_{12}]$
369.2.s.a	$369$	$2$	369.s	369.s	$15$	$320$	$40$	$2.946$		None		$4$	$0$	$-5$	$-18$	$-7$	$-3$			$\mathrm{SU}(2)[C_{15}]$
369.2.u.a	$369$	$2$	369.u	41.g	$20$	$24$	$3$	$2.946$		None		$2$	$0$	$10$	$0$	$10$	$-8$			$\mathrm{SU}(2)[C_{20}]$
369.2.u.b	$369$	$2$	369.u	41.g	$20$	$48$	$6$	$2.946$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
369.2.u.c	$369$	$2$	369.u	41.g	$20$	$64$	$8$	$2.946$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
369.2.v.a	$369$	$2$	369.v	369.v	$24$	$320$	$40$	$2.946$		None		$4$	$0$	$-12$	$-4$	$-12$	$-4$			$\mathrm{SU}(2)[C_{24}]$
369.2.z.a	$369$	$2$	369.z	369.z	$30$	$320$	$40$	$2.946$		None		$4$	$0$	$-1$	$0$	$1$	$-5$			$\mathrm{SU}(2)[C_{30}]$
369.2.ba.a	$369$	$2$	369.ba	123.o	$40$	$112$	$7$	$2.946$		None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{40}]$
369.2.ba.b	$369$	$2$	369.ba	123.o	$40$	$112$	$7$	$2.946$		None		$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{40}]$
369.2.bc.a	$369$	$2$	369.bc	369.ac	$60$	$640$	$40$	$2.946$		None		$4$	$0$	$-10$	$-18$	$-10$	$-8$			$\mathrm{SU}(2)[C_{60}]$
369.2.bf.a	$369$	$2$	369.bf	369.af	$120$	$1280$	$40$	$2.946$		None		$4$	$0$	$-48$	$-36$	$-48$	$-16$			$\mathrm{SU}(2)[C_{120}]$
369.3.b.a	$369$	$3$	369.b	123.b	$2$	$28$	$28$	$10.055$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
369.3.c.a	$369$	$3$	369.c	3.b	$2$	$28$	$28$	$10.055$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
369.3.g.a	$369$	$3$	369.g	123.f	$4$	$56$	$28$	$10.055$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
369.3.j.a	$369$	$3$	369.j	9.d	$6$	$160$	$80$	$10.055$		None		$2$	$0$	$0$	$-2$	$-18$	$2$			$\mathrm{SU}(2)[C_{6}]$
369.3.k.a	$369$	$3$	369.k	369.k	$6$	$164$	$82$	$10.055$		None		$4$	$0$	$-6$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.