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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	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
603.1.b.a	$603$	$1$	603.b	67.b	$2$	$1$	$1$	$0.301$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-67}) $	$\Q(\sqrt{201}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{16}-2q^{19}+q^{25}-2q^{37}+\cdots$
603.1.x.a	$603$	$1$	603.x	67.f	$22$	$10$	$1$	$0.301$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{22}^{5}q^{4}+(\zeta_{22}^{2}+\zeta_{22}^{3})q^{7}+(-\zeta_{22}+\cdots)q^{13}+\cdots$
603.2.a.a	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-2q^{5}-2q^{7}+4q^{10}+\cdots$
603.2.a.b	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+4q^{7}+3q^{8}-2q^{10}+\cdots$
603.2.a.c	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{5}-3q^{7}+3q^{8}-3q^{10}+\cdots$
603.2.a.d	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}+4q^{7}-3q^{8}-2q^{10}+\cdots$
603.2.a.e	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-5q^{7}-3q^{8}+q^{10}+\cdots$
603.2.a.f	$603$	$2$	603.a	1.a	$1$	$1$	$1$	$4.815$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+6q^{11}+4q^{13}-4q^{16}+\cdots$
603.2.a.g	$603$	$2$	603.a	1.a	$1$	$2$	$2$	$4.815$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
603.2.a.h	$603$	$2$	603.a	1.a	$1$	$2$	$2$	$4.815$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$6$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+3q^{5}+(1-3\beta )q^{7}+\cdots$
603.2.a.i	$603$	$2$	603.a	1.a	$1$	$3$	$3$	$4.815$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
603.2.a.j	$603$	$2$	603.a	1.a	$1$	$4$	$4$	$4.815$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-2\beta _{1}-\beta _{3})q^{5}+\cdots$
603.2.a.k	$603$	$2$	603.a	1.a	$1$	$5$	$5$	$4.815$	5.5.1025428.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots$
603.2.a.l	$603$	$2$	603.a	1.a	$1$	$6$	$6$	$4.815$	6.6.2482793472.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots$
603.2.d.a	$603$	$2$	603.d	201.d	$2$	$4$	$4$	$4.815$	$\Q(\sqrt{-2}, \sqrt{67})$	$_{}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+4q^{16}+\beta _{1}q^{17}+\beta _{3}q^{19}+\cdots$
603.2.d.b	$603$	$2$	603.d	201.d	$2$	$20$	$20$	$4.815$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{17}q^{2}+(2+\beta _{6})q^{4}+\beta _{12}q^{5}-\beta _{3}q^{7}+\cdots$
603.2.e.a	$603$	$2$	603.e	9.c	$3$	$66$	$33$	$4.815$		$_{}$	None	None		$2$	$0$	$-7$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{3}]$
603.2.e.b	$603$	$2$	603.e	9.c	$3$	$66$	$33$	$4.815$		$_{}$	None	None		$2$	$0$	$7$	$0$	$18$	$0$			$\mathrm{SU}(2)[C_{3}]$
603.2.f.a	$603$	$2$	603.f	603.f	$3$	$2$	$1$	$4.815$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$-3$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
603.2.f.b	$603$	$2$	603.f	603.f	$3$	$2$	$1$	$4.815$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
603.2.f.c	$603$	$2$	603.f	603.f	$3$	$128$	$64$	$4.815$		$_{}$	None	None		$2$	$0$	$1$	$-3$	$5$	$-8$			$\mathrm{SU}(2)[C_{3}]$
603.2.g.a	$603$	$2$	603.g	67.c	$3$	$2$	$1$	$4.815$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+4\zeta_{6}q^{7}+(7-7\zeta_{6})q^{13}+\cdots$
603.2.g.b	$603$	$2$	603.g	67.c	$3$	$2$	$1$	$4.815$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$8$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+4q^{5}-4\zeta_{6}q^{7}+\cdots$
603.2.g.c	$603$	$2$	603.g	67.c	$3$	$4$	$2$	$4.815$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(2+2\beta _{2}+\cdots)q^{5}+\cdots$
603.2.g.d	$603$	$2$	603.g	67.c	$3$	$4$	$2$	$4.815$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-2+\cdots)q^{5}+\cdots$
603.2.g.e	$603$	$2$	603.g	67.c	$3$	$10$	$5$	$4.815$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{8})q^{4}+(1+\cdots)q^{5}+\cdots$
603.2.g.f	$603$	$2$	603.g	67.c	$3$	$10$	$5$	$4.815$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{9}q^{2}+(\beta _{1}-2\beta _{4}-2\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots$
603.2.g.g	$603$	$2$	603.g	67.c	$3$	$10$	$5$	$4.815$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\beta _{8}+\cdots)q^{4}+\cdots$
603.2.g.h	$603$	$2$	603.g	67.c	$3$	$12$	$6$	$4.815$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$6$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{3}+2\beta _{6}+\beta _{9})q^{4}+\beta _{10}q^{5}+\cdots$
603.2.h.a	$603$	$2$	603.h	603.h	$3$	$2$	$1$	$4.815$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+(-3+\cdots)q^{5}+\cdots$
603.2.h.b	$603$	$2$	603.h	603.h	$3$	$2$	$1$	$4.815$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots$
603.2.h.c	$603$	$2$	603.h	603.h	$3$	$128$	$64$	$4.815$		$_{}$	None	None		$2$	$0$	$-2$	$-3$	$5$	$4$			$\mathrm{SU}(2)[C_{3}]$
603.2.k.a	$603$	$2$	603.k	603.k	$6$	$132$	$66$	$4.815$		$_{}$	None	None		$2$	$0$	$-3$	$-3$	$3$	$0$			$\mathrm{SU}(2)[C_{6}]$
603.2.l.a	$603$	$2$	603.l	603.l	$6$	$132$	$66$	$4.815$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
603.2.m.a	$603$	$2$	603.m	201.f	$6$	$44$	$22$	$4.815$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
603.2.t.a	$603$	$2$	603.t	603.t	$6$	$132$	$66$	$4.815$		$_{}$	None	None		$2$	$0$	$-6$	$3$	$-3$	$-6$			$\mathrm{SU}(2)[C_{6}]$
603.2.u.a	$603$	$2$	603.u	67.e	$11$	$10$	$1$	$4.815$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$9$	$7$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}-\zeta_{22}^{4}+\cdots)q^{2}+\cdots$
603.2.u.b	$603$	$2$	603.u	67.e	$11$	$10$	$1$	$4.815$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$6$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1+\zeta_{22}^{2}+\zeta_{22}^{4}-\zeta_{22}^{7}+\zeta_{22}^{8}+\cdots)q^{2}+\cdots$
603.2.u.c	$603$	$2$	603.u	67.e	$11$	$20$	$2$	$4.815$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$0$	$-1$	$-8$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1+\beta _{7}-\beta _{8}-\beta _{9}+\beta _{11}+\beta _{13}+\cdots)q^{2}+\cdots$
603.2.u.d	$603$	$2$	603.u	67.e	$11$	$50$	$5$	$4.815$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$2$			$\mathrm{SU}(2)[C_{11}]$
603.2.u.e	$603$	$2$	603.u	67.e	$11$	$70$	$7$	$4.815$		$_{}$	None	None		$2$	$0$	$2$	$0$	$2$	$-10$			$\mathrm{SU}(2)[C_{11}]$
603.2.u.f	$603$	$2$	603.u	67.e	$11$	$120$	$12$	$4.815$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{11}]$
603.2.v.a	$603$	$2$	603.v	201.j	$22$	$240$	$24$	$4.815$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
603.2.y.a	$603$	$2$	603.y	603.y	$33$	$1320$	$66$	$4.815$		$_{}$	None	None		$2$	$0$	$-5$	$-19$	$-14$	$-11$			$\mathrm{SU}(2)[C_{33}]$
603.2.z.a	$603$	$2$	603.z	67.g	$33$	$20$	$1$	$4.815$	$\Q(\zeta_{33})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{33}]$	$q-2\zeta_{33}^{8}q^{4}+(\zeta_{33}+3\zeta_{33}^{7}+3\zeta_{33}^{12}+\cdots)q^{7}+\cdots$
603.2.z.b	$603$	$2$	603.z	67.g	$33$	$100$	$5$	$4.815$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$2$	$1$			$\mathrm{SU}(2)[C_{33}]$
603.2.z.c	$603$	$2$	603.z	67.g	$33$	$100$	$5$	$4.815$		$_{}$	None	None		$2$	$0$	$24$	$0$	$16$	$-24$			$\mathrm{SU}(2)[C_{33}]$
603.2.z.d	$603$	$2$	603.z	67.g	$33$	$120$	$6$	$4.815$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$-2$	$5$			$\mathrm{SU}(2)[C_{33}]$
603.2.z.e	$603$	$2$	603.z	67.g	$33$	$200$	$10$	$4.815$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{33}]$
603.2.ba.a	$603$	$2$	603.ba	603.aa	$33$	$1320$	$66$	$4.815$		$_{}$	None	None		$2$	$0$	$-14$	$-19$	$-14$	$-11$			$\mathrm{SU}(2)[C_{33}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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.