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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 163 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
693.1.h.a	$693$	$1$	693.h	231.h	$2$	$4$	$4$	$0.346$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+\cdots$
693.1.o.a	$693$	$1$	693.o	693.o	$6$	$4$	$2$	$0.346$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{5}q^{6}+\cdots$
693.1.bl.a	$693$	$1$	693.bl	693.al	$6$	$4$	$2$	$0.346$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-q^{3}+\zeta_{12}q^{6}-\zeta_{12}^{3}q^{7}+\cdots$
693.1.bp.a	$693$	$1$	693.bp	231.r	$10$	$16$	$4$	$0.346$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{2}+\zeta_{40}^{8}+\cdots)q^{4}+\cdots$
693.1.br.a	$693$	$1$	693.br	77.j	$10$	$4$	$1$	$0.346$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-1$		$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
693.1.br.b	$693$	$1$	693.br	77.j	$10$	$8$	$2$	$0.346$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(-\zeta_{20}^{2}+\zeta_{20}^{6}+\cdots)q^{4}+\cdots$
693.2.a.a	$693$	$2$	693.a	1.a	$1$	$1$	$1$	$5.534$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots$
693.2.a.b	$693$	$2$	693.a	1.a	$1$	$1$	$1$	$5.534$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{5}+q^{7}+q^{11}-4q^{13}+\cdots$
693.2.a.c	$693$	$2$	693.a	1.a	$1$	$1$	$1$	$5.534$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-q^{7}+q^{11}-4q^{13}+\cdots$
693.2.a.d	$693$	$2$	693.a	1.a	$1$	$1$	$1$	$5.534$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots$
693.2.a.e	$693$	$2$	693.a	1.a	$1$	$2$	$2$	$5.534$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+\cdots$
693.2.a.f	$693$	$2$	693.a	1.a	$1$	$2$	$2$	$5.534$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots$
693.2.a.g	$693$	$2$	693.a	1.a	$1$	$2$	$2$	$5.534$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}-q^{5}-q^{7}-3q^{8}+\cdots$
693.2.a.h	$693$	$2$	693.a	1.a	$1$	$2$	$2$	$5.534$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}+2q^{5}+q^{7}-\beta q^{8}+\cdots$
693.2.a.i	$693$	$2$	693.a	1.a	$1$	$2$	$2$	$5.534$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+q^{5}-q^{7}+3q^{8}+\cdots$
693.2.a.j	$693$	$2$	693.a	1.a	$1$	$2$	$2$	$5.534$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(3+\beta )q^{4}-3q^{5}+q^{7}+(5+\cdots)q^{8}+\cdots$
693.2.a.k	$693$	$2$	693.a	1.a	$1$	$2$	$2$	$5.534$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots$
693.2.a.l	$693$	$2$	693.a	1.a	$1$	$3$	$3$	$5.534$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$
693.2.a.m	$693$	$2$	693.a	1.a	$1$	$3$	$3$	$5.534$	3.3.837.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
693.2.c.a	$693$	$2$	693.c	77.b	$2$	$2$	$2$	$5.534$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}-5q^{4}+\beta q^{7}+3\beta q^{8}+(-2+\cdots)q^{11}+\cdots$
693.2.c.b	$693$	$2$	693.c	77.b	$2$	$4$	$4$	$5.534$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}-2\beta _{2}q^{8}+\cdots$
693.2.c.c	$693$	$2$	693.c	77.b	$2$	$4$	$4$	$5.534$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+q^{4}-\beta _{3}q^{7}+3\beta _{1}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots$
693.2.c.d	$693$	$2$	693.c	77.b	$2$	$12$	$12$	$5.534$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-231}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{2}+(-2+\beta _{1})q^{4}+\beta _{4}q^{5}+\beta _{6}q^{7}+\cdots$
693.2.c.e	$693$	$2$	693.c	77.b	$2$	$16$	$16$	$5.534$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+(-1+\beta _{4})q^{4}-\beta _{1}q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots$
693.2.e.a	$693$	$2$	693.e	21.c	$2$	$24$	$24$	$5.534$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
693.2.g.a	$693$	$2$	693.g	33.d	$2$	$24$	$24$	$5.534$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
693.2.i.a	$693$	$2$	693.i	7.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots$
693.2.i.b	$693$	$2$	693.i	7.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
693.2.i.c	$693$	$2$	693.i	7.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$
693.2.i.d	$693$	$2$	693.i	7.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$
693.2.i.e	$693$	$2$	693.i	7.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(-1-2\zeta_{6})q^{7}+\cdots$
693.2.i.f	$693$	$2$	693.i	7.c	$3$	$4$	$2$	$5.534$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
693.2.i.g	$693$	$2$	693.i	7.c	$3$	$6$	$3$	$5.534$	6.0.1783323.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}-\beta _{5})q^{2}+(-1-\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots$
693.2.i.h	$693$	$2$	693.i	7.c	$3$	$6$	$3$	$5.534$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$
693.2.i.i	$693$	$2$	693.i	7.c	$3$	$8$	$4$	$5.534$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{6})q^{4}+\cdots$
693.2.i.j	$693$	$2$	693.i	7.c	$3$	$10$	$5$	$5.534$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$-4$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-2-2\beta _{2}-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
693.2.i.k	$693$	$2$	693.i	7.c	$3$	$12$	$6$	$5.534$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{2}+(-2+2\beta _{4}-\beta _{8})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
693.2.i.l	$693$	$2$	693.i	7.c	$3$	$12$	$6$	$5.534$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+(-2+2\beta _{4}-\beta _{8})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
693.2.j.a	$693$	$2$	693.j	9.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$3$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
693.2.j.b	$693$	$2$	693.j	9.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$-3$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
693.2.j.c	$693$	$2$	693.j	9.c	$3$	$2$	$1$	$5.534$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
693.2.j.d	$693$	$2$	693.j	9.c	$3$	$6$	$3$	$5.534$	6.0.4406832.1	$_{}$	None	None		$2$	$0$	$1$	$9$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}+\beta _{5})q^{2}+(2-\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
693.2.j.e	$693$	$2$	693.j	9.c	$3$	$12$	$6$	$5.534$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$-1$	$-1$	$12$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{8})q^{2}+(\beta _{2}-\beta _{8})q^{3}+(-2+\cdots)q^{4}+\cdots$
693.2.j.f	$693$	$2$	693.j	9.c	$3$	$18$	$9$	$5.534$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-1$	$1$	$-6$	$-9$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+\beta _{13}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
693.2.j.g	$693$	$2$	693.j	9.c	$3$	$20$	$10$	$5.534$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$-8$	$-10$	$-10$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+\beta _{4}q^{3}+(\beta _{7}+\beta _{12}-\beta _{13}+\cdots)q^{4}+\cdots$
693.2.j.h	$693$	$2$	693.j	9.c	$3$	$28$	$14$	$5.534$		$_{}$	None	None		$2$	$0$	$-1$	$-2$	$-4$	$14$			$\mathrm{SU}(2)[C_{3}]$
693.2.j.i	$693$	$2$	693.j	9.c	$3$	$30$	$15$	$5.534$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$1$	$15$			$\mathrm{SU}(2)[C_{3}]$
693.2.k.a	$693$	$2$	693.k	63.g	$3$	$6$	$3$	$5.534$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots$
693.2.k.b	$693$	$2$	693.k	63.g	$3$	$74$	$37$	$5.534$		$_{}$	None	None		$2$	$0$	$0$	$0$	$14$	$-1$			$\mathrm{SU}(2)[C_{3}]$
693.2.k.c	$693$	$2$	693.k	63.g	$3$	$80$	$40$	$5.534$		$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$-1$			$\mathrm{SU}(2)[C_{3}]$

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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.