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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 115 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
352.1.t.a	$352$	$1$	352.t	88.l	$10$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots$
352.2.a.a	$352$	$2$	352.a	1.a	$1$	$1$	$1$	$2.811$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+q^{11}-6q^{13}+\cdots$
352.2.a.b	$352$	$2$	352.a	1.a	$1$	$1$	$1$	$2.811$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+4q^{7}-2q^{9}-q^{11}+\cdots$
352.2.a.c	$352$	$2$	352.a	1.a	$1$	$1$	$1$	$2.811$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots$
352.2.a.d	$352$	$2$	352.a	1.a	$1$	$1$	$1$	$2.811$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-4q^{7}-2q^{9}+q^{11}+\cdots$
352.2.a.e	$352$	$2$	352.a	1.a	$1$	$1$	$1$	$2.811$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots$
352.2.a.f	$352$	$2$	352.a	1.a	$1$	$1$	$1$	$2.811$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}-q^{11}-6q^{13}+\cdots$
352.2.a.g	$352$	$2$	352.a	1.a	$1$	$2$	$2$	$2.811$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots$
352.2.a.h	$352$	$2$	352.a	1.a	$1$	$2$	$2$	$2.811$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}+q^{11}+\cdots$
352.2.c.a	$352$	$2$	352.c	8.b	$2$	$10$	$10$	$2.811$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{5}-\beta _{6})q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
352.2.e.a	$352$	$2$	352.e	44.c	$2$	$12$	$12$	$2.811$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{5}q^{5}+\beta _{8}q^{7}+\beta _{3}q^{9}+\cdots$
352.2.g.a	$352$	$2$	352.g	88.g	$2$	$2$	$2$	$2.811$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{3}+q^{9}+(3+\beta )q^{11}+4\beta q^{17}+\cdots$
352.2.g.b	$352$	$2$	352.g	88.g	$2$	$8$	$8$	$2.811$	8.0.$\cdots$.6	$_{}$	None	None		$4$	$0$	$0$	$8$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+\beta _{6}q^{5}-\beta _{7}q^{7}+2\beta _{1}q^{9}+\cdots$
352.2.m.a	$352$	$2$	352.m	11.c	$5$	$4$	$1$	$2.811$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-6$	$-10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-2-2\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
352.2.m.b	$352$	$2$	352.m	11.c	$5$	$4$	$1$	$2.811$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-6$	$10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}+\zeta_{10}^{3})q^{3}+(-2-2\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
352.2.m.c	$352$	$2$	352.m	11.c	$5$	$8$	$2$	$2.811$	8.0.484000000.9	$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{3}+(\beta _{2}+\beta _{3}+\beta _{5})q^{5}+(\beta _{4}+\beta _{7})q^{7}+\cdots$
352.2.m.d	$352$	$2$	352.m	11.c	$5$	$8$	$2$	$2.811$	8.0.484000000.6	$_{}$	None	None		$4$	$0$	$0$	$0$	$14$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(1+\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots$
352.2.m.e	$352$	$2$	352.m	11.c	$5$	$12$	$3$	$2.811$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{5}-\beta _{8})q^{3}+\beta _{9}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
352.2.m.f	$352$	$2$	352.m	11.c	$5$	$12$	$3$	$2.811$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}+\beta _{8})q^{3}+\beta _{9}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
352.2.n.a	$352$	$2$	352.n	32.g	$8$	$160$	$40$	$2.811$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
352.2.q.a	$352$	$2$	352.q	352.q	$8$	$184$	$46$	$2.811$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$-8$	$0$			$\mathrm{SU}(2)[C_{8}]$
352.2.s.a	$352$	$2$	352.s	88.k	$10$	$8$	$2$	$2.811$	8.0.64000000.1	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(1+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(2\beta _{1}+\cdots)q^{9}+\cdots$
352.2.s.b	$352$	$2$	352.s	88.k	$10$	$32$	$8$	$2.811$		$_{}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
352.2.u.a	$352$	$2$	352.u	44.g	$10$	$48$	$12$	$2.811$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
352.2.w.a	$352$	$2$	352.w	88.o	$10$	$40$	$10$	$2.811$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$10$			$\mathrm{SU}(2)[C_{10}]$
352.2.bc.a	$352$	$2$	352.bc	352.ac	$40$	$736$	$46$	$2.811$		$_{}$	None	None		$4$	$0$	$-20$	$-12$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
352.2.bf.a	$352$	$2$	352.bf	352.af	$40$	$736$	$46$	$2.811$		$_{}$	None	None		$4$	$0$	$-12$	$-12$	$-12$	$-12$			$\mathrm{SU}(2)[C_{40}]$
352.3.b.a	$352$	$3$	352.b	88.b	$2$	$1$	$1$	$9.591$	$\Q$	$_{}$	$\Q(\sqrt{-22}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}-11q^{11}+18q^{13}-6q^{19}+\cdots$
352.3.b.b	$352$	$3$	352.b	88.b	$2$	$1$	$1$	$9.591$	$\Q$	$_{}$	$\Q(\sqrt{-22}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}+11q^{11}-18q^{13}+6q^{19}+\cdots$
352.3.b.c	$352$	$3$	352.b	88.b	$2$	$20$	$20$	$9.591$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{32}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{12}q^{5}-\beta _{2}q^{7}+(-4-\beta _{4}+\cdots)q^{9}+\cdots$
352.3.d.a	$352$	$3$	352.d	4.b	$2$	$8$	$8$	$9.591$	8.0.1499238400.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(-1+\beta _{2})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
352.3.d.b	$352$	$3$	352.d	4.b	$2$	$12$	$12$	$9.591$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{1}q^{5}+(-\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{7}+\cdots$
352.3.f.a	$352$	$3$	352.f	8.d	$2$	$20$	$20$	$9.591$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{32}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{6}q^{5}-\beta _{5}q^{7}+(3+\beta _{15}+\cdots)q^{9}+\cdots$
352.3.h.a	$352$	$3$	352.h	11.b	$2$	$12$	$12$	$9.591$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(4+\beta _{1}+\cdots)q^{9}+\cdots$
352.3.h.b	$352$	$3$	352.h	11.b	$2$	$12$	$12$	$9.591$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+\beta _{2}q^{5}+\beta _{8}q^{7}+(4+\beta _{3}+\cdots)q^{9}+\cdots$
352.3.o.a	$352$	$3$	352.o	352.o	$8$	$376$	$94$	$9.591$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$-8$	$0$			$\mathrm{SU}(2)[C_{8}]$
352.3.p.a	$352$	$3$	352.p	32.h	$8$	$320$	$80$	$9.591$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
352.3.r.a	$352$	$3$	352.r	11.d	$10$	$48$	$12$	$9.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
352.3.r.b	$352$	$3$	352.r	11.d	$10$	$48$	$12$	$9.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
352.3.t.a	$352$	$3$	352.t	88.l	$10$	$8$	$2$	$9.591$	8.0.64000000.1	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{10}]$	$q+(-1-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4})q^{3}+(2\beta _{1}+\cdots)q^{9}+\cdots$
352.3.t.b	$352$	$3$	352.t	88.l	$10$	$80$	$20$	$9.591$		$_{}$	None	None		$4$	$0$	$0$	$10$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
352.3.v.a	$352$	$3$	352.v	44.h	$10$	$48$	$12$	$9.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
352.3.v.b	$352$	$3$	352.v	44.h	$10$	$48$	$12$	$9.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
352.3.x.a	$352$	$3$	352.x	88.p	$10$	$88$	$22$	$9.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$10$			$\mathrm{SU}(2)[C_{10}]$
352.3.bd.a	$352$	$3$	352.bd	352.ad	$40$	$1504$	$94$	$9.591$		$_{}$	None	None		$4$	$0$	$-12$	$-12$	$-12$	$-12$			$\mathrm{SU}(2)[C_{40}]$
352.3.be.a	$352$	$3$	352.be	352.ae	$40$	$1504$	$94$	$9.591$		$_{}$	None	None		$4$	$0$	$-20$	$-12$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
352.4.a.a	$352$	$4$	352.a	1.a	$1$	$3$	$3$	$20.769$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-5$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots$
352.4.a.b	$352$	$4$	352.a	1.a	$1$	$3$	$3$	$20.769$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-5$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots$
352.4.a.c	$352$	$4$	352.a	1.a	$1$	$4$	$4$	$20.769$	4.4.2767476.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-9$	$-11$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{3}+(-3-\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
352.4.a.d	$352$	$4$	352.a	1.a	$1$	$4$	$4$	$20.769$	4.4.474868.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-11$	$-28$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{3}+(-3-\beta _{2}+\beta _{3})q^{5}+\cdots$

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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.