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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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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
348.2.a.a	$348$	$2$	348.a	1.a	$1$	$1$	$1$	$2.779$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots$
348.2.a.b	$348$	$2$	348.a	1.a	$1$	$1$	$1$	$2.779$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots$
348.2.a.c	$348$	$2$	348.a	1.a	$1$	$1$	$1$	$2.779$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-3q^{7}+q^{9}-q^{11}-3q^{13}+\cdots$
348.2.a.d	$348$	$2$	348.a	1.a	$1$	$1$	$1$	$2.779$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots$
348.2.b.a	$348$	$2$	348.b	348.b	$2$	$8$	$8$	$2.779$	8.0.12960000.1	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{4}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$
348.2.b.b	$348$	$2$	348.b	348.b	$2$	$12$	$12$	$2.779$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$\Q(\sqrt{-29}) $		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{2}-\beta _{11}q^{3}-2q^{4}+\beta _{9}q^{5}+\cdots$
348.2.b.c	$348$	$2$	348.b	348.b	$2$	$12$	$12$	$2.779$	12.0.$\cdots$.3	$\Q(\sqrt{-87}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{6}q^{2}+\beta _{4}q^{3}+\beta _{5}q^{4}-\beta _{3}q^{6}+\cdots$
348.2.b.d	$348$	$2$	348.b	348.b	$2$	$24$	$24$	$2.779$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
348.2.c.a	$348$	$2$	348.c	12.b	$2$	$16$	$16$	$2.779$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{1}q^{3}+(\beta _{2}+\beta _{9}+\beta _{11}+\cdots)q^{4}+\cdots$
348.2.c.b	$348$	$2$	348.c	12.b	$2$	$40$	$40$	$2.779$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
348.2.h.a	$348$	$2$	348.h	29.b	$2$	$2$	$2$	$2.779$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-2q^{5}-3q^{7}-q^{9}-3iq^{11}+\cdots$
348.2.h.b	$348$	$2$	348.h	29.b	$2$	$2$	$2$	$2.779$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-2q^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots$
348.2.h.c	$348$	$2$	348.h	29.b	$2$	$2$	$2$	$2.779$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$8$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+4q^{5}+q^{7}-q^{9}-5iq^{11}+\cdots$
348.2.i.a	$348$	$2$	348.i	116.e	$4$	$60$	$30$	$2.779$		None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
348.2.l.a	$348$	$2$	348.l	87.f	$4$	$20$	$10$	$2.779$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{14}q^{3}+\beta _{19}q^{5}-\beta _{8}q^{7}-\beta _{3}q^{9}+\cdots$
348.2.m.a	$348$	$2$	348.m	29.d	$7$	$12$	$2$	$2.779$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-2$	$-5$	$2$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{11}q^{3}+(-1+\beta _{2}-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$
348.2.m.b	$348$	$2$	348.m	29.d	$7$	$12$	$2$	$2.779$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$2$	$9$	$2$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{8}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
348.2.n.a	$348$	$2$	348.n	29.e	$14$	$36$	$6$	$2.779$		None		$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{14}]$
348.2.s.a	$348$	$2$	348.s	348.s	$14$	$336$	$56$	$2.779$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
348.2.t.a	$348$	$2$	348.t	348.t	$14$	$336$	$56$	$2.779$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
348.2.u.a	$348$	$2$	348.u	87.k	$28$	$120$	$10$	$2.779$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
348.2.x.a	$348$	$2$	348.x	116.l	$28$	$360$	$30$	$2.779$		None		$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
348.3.d.a	$348$	$3$	348.d	3.b	$2$	$4$	$4$	$9.482$	$\Q(\sqrt{-5}, \sqrt{-29})$	None		$2$	$0$	$0$	$8$	$0$	$-22$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+\beta _{2})q^{3}-2\beta _{2}q^{5}+(-6+\beta _{3})q^{7}+\cdots$
348.3.d.b	$348$	$3$	348.d	3.b	$2$	$14$	$14$	$9.482$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$26$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{11}q^{5}+(2+\beta _{4})q^{7}+\beta _{2}q^{9}+\cdots$
348.3.e.a	$348$	$3$	348.e	87.d	$2$	$4$	$4$	$9.482$	$\Q(i, \sqrt{29})$	None		$4$	$0$	$0$	$0$	$0$	$-20$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-3\beta _{1}q^{3}-\beta _{2}q^{5}-5q^{7}-9q^{9}-2\beta _{3}q^{11}+\cdots$
348.3.e.b	$348$	$3$	348.e	87.d	$2$	$16$	$16$	$9.482$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$12$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}-\beta _{5}q^{5}+(1+\beta _{4})q^{7}+(1-\beta _{7}+\cdots)q^{9}+\cdots$
348.3.f.a	$348$	$3$	348.f	4.b	$2$	$56$	$56$	$9.482$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
348.3.g.a	$348$	$3$	348.g	116.d	$2$	$60$	$60$	$9.482$		None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{2}]$
348.3.j.a	$348$	$3$	348.j	29.c	$4$	$20$	$10$	$9.482$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{3}+(-\beta _{1}+\beta _{6}-\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots$
348.3.k.a	$348$	$3$	348.k	348.k	$4$	$232$	$116$	$9.482$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
348.3.o.a	$348$	$3$	348.o	116.h	$14$	$360$	$60$	$9.482$		None		$4$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{14}]$
348.3.p.a	$348$	$3$	348.p	116.j	$14$	$360$	$60$	$9.482$		None		$4$	$0$	$4$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{14}]$
348.3.q.a	$348$	$3$	348.q	87.h	$14$	$120$	$20$	$9.482$		None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{14}]$
348.3.r.a	$348$	$3$	348.r	87.j	$14$	$120$	$20$	$9.482$		None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{14}]$
348.3.v.a	$348$	$3$	348.v	348.v	$28$	$1392$	$116$	$9.482$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
348.3.w.a	$348$	$3$	348.w	29.f	$28$	$120$	$10$	$9.482$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
348.4.a.a	$348$	$4$	348.a	1.a	$1$	$1$	$1$	$20.533$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$-9$	$21$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-9q^{5}+21q^{7}+9q^{9}-66q^{11}+\cdots$
348.4.a.b	$348$	$4$	348.a	1.a	$1$	$2$	$2$	$20.533$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$0$	$6$	$-2$	$-40$	$-$	$2$	$\mathrm{SU}(2)$	$q+3q^{3}+(-1-\beta )q^{5}+(-20+3\beta )q^{7}+\cdots$
348.4.a.c	$348$	$4$	348.a	1.a	$1$	$3$	$3$	$20.533$	3.3.189021.1	None	✓	$1$	$0$	$0$	$9$	$19$	$9$	$+$	$2$	$\mathrm{SU}(2)$	$q+3q^{3}+(6-\beta _{2})q^{5}+(3+\beta _{1}-\beta _{2})q^{7}+\cdots$
348.4.a.d	$348$	$4$	348.a	1.a	$1$	$4$	$4$	$20.533$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$0$	$-12$	$-1$	$17$	$+$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots$
348.4.a.e	$348$	$4$	348.a	1.a	$1$	$4$	$4$	$20.533$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$0$	$-12$	$9$	$-11$	$-$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(2-\beta _{2})q^{5}+(-3+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
348.4.h.a	$348$	$4$	348.h	29.b	$2$	$14$	$14$	$20.533$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$0$	$24$	$-12$		$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}+(2+\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots$
348.4.l.a	$348$	$4$	348.l	87.f	$4$	$60$	$30$	$20.533$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
348.4.m.a	$348$	$4$	348.m	29.d	$7$	$48$	$8$	$20.533$		None		$2$	$0$	$0$	$-24$	$-21$	$-6$			$\mathrm{SU}(2)[C_{7}]$
348.4.m.b	$348$	$4$	348.m	29.d	$7$	$48$	$8$	$20.533$		None		$2$	$0$	$0$	$24$	$41$	$-6$			$\mathrm{SU}(2)[C_{7}]$
348.4.n.a	$348$	$4$	348.n	29.e	$14$	$84$	$14$	$20.533$		None		$2$	$0$	$0$	$0$	$-24$	$12$			$\mathrm{SU}(2)[C_{14}]$
348.5.d.a	$348$	$5$	348.d	3.b	$2$	$38$	$38$	$35.973$		None		$2$	$0$	$0$	$-18$	$0$	$108$			$\mathrm{SU}(2)[C_{2}]$
348.5.e.a	$348$	$5$	348.e	87.d	$2$	$40$	$40$	$35.973$		None		$4$	$0$	$0$	$0$	$0$	$80$			$\mathrm{SU}(2)[C_{2}]$
348.5.j.a	$348$	$5$	348.j	29.c	$4$	$40$	$20$	$35.973$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
348.6.a.a	$348$	$6$	348.a	1.a	$1$	$6$	$6$	$55.814$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$0$	$-54$	$-36$	$117$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-9q^{3}+(-6-\beta _{2})q^{5}+(20-\beta _{5})q^{7}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 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.