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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 185 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
114.2.a.a	$114$	$2$	114.a	1.a	$1$	$1$	$1$	$0.910$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots$
114.2.a.b	$114$	$2$	114.a	1.a	$1$	$1$	$1$	$0.910$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
114.2.a.c	$114$	$2$	114.a	1.a	$1$	$1$	$1$	$0.910$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
114.2.b.a	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$-2$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots$
114.2.b.b	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$3$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots$
114.2.b.c	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-3$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(2-4\zeta_{6})q^{5}+\cdots$
114.2.b.d	$114$	$2$	114.b	57.d	$2$	$2$	$2$	$0.910$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$2$	$2$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots$
114.2.e.a	$114$	$2$	114.e	19.c	$3$	$2$	$1$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$4$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
114.2.e.b	$114$	$2$	114.e	19.c	$3$	$2$	$1$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$1$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
114.2.h.a	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$-3$	$-6$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
114.2.h.b	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
114.2.h.c	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-3$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
114.2.h.d	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
114.2.h.e	$114$	$2$	114.h	57.f	$6$	$4$	$2$	$0.910$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$-2$	$4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
114.2.h.f	$114$	$2$	114.h	57.f	$6$	$4$	$2$	$0.910$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$2$	$2$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
114.2.i.a	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$0$	$-9$	$9$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
114.2.i.b	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$0$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
114.2.i.c	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$0$	$3$	$-3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$
114.2.i.d	$114$	$2$	114.i	19.e	$9$	$6$	$1$	$0.910$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$0$	$9$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$
114.2.l.a	$114$	$2$	114.l	57.j	$18$	$18$	$3$	$0.910$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(-\beta _{6}-\beta _{7})q^{2}+(\beta _{1}-\beta _{17})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots$
114.2.l.b	$114$	$2$	114.l	57.j	$18$	$18$	$3$	$0.910$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}-\beta _{7}q^{4}+(\beta _{9}-\beta _{17})q^{5}+\cdots$
114.3.c.a	$114$	$3$	114.c	3.b	$2$	$12$	$12$	$3.106$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-4$	$0$	$-8$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{9}q^{3}-2q^{4}+\beta _{4}q^{5}+(1+\cdots)q^{6}+\cdots$
114.3.d.a	$114$	$3$	114.d	19.b	$2$	$8$	$8$	$3.106$	8.0.$\cdots$.3	None		$2$	$0$	$0$	$0$	$4$	$-12$		$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{4}q^{3}-2q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots$
114.3.f.a	$114$	$3$	114.f	19.d	$6$	$8$	$4$	$3.106$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$-12$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+(-1-\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots$
114.3.f.b	$114$	$3$	114.f	19.d	$6$	$8$	$4$	$3.106$	8.0.$\cdots$.10	None		$2$	$0$	$0$	$12$	$4$	$-24$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(2-\beta _{4})q^{3}+(2-2\beta _{4})q^{4}+\cdots$
114.3.g.a	$114$	$3$	114.g	57.h	$6$	$24$	$12$	$3.106$		None		$4$	$0$	$0$	$-2$	$0$	$8$			$\mathrm{SU}(2)[C_{6}]$
114.3.j.a	$114$	$3$	114.j	19.f	$18$	$12$	$2$	$3.106$	12.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$0$	$18$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q-\beta _{11}q^{2}+(2\beta _{2}-\beta _{8})q^{3}-2\beta _{4}q^{4}+\cdots$
114.3.j.b	$114$	$3$	114.j	19.f	$18$	$24$	$4$	$3.106$		None		$2$	$0$	$0$	$0$	$0$	$18$			$\mathrm{SU}(2)[C_{18}]$
114.3.k.a	$114$	$3$	114.k	57.l	$18$	$84$	$14$	$3.106$		None		$4$	$0$	$0$	$6$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
114.4.a.a	$114$	$4$	114.a	1.a	$1$	$1$	$1$	$6.726$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$-19$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-19q^{5}+6q^{6}+\cdots$
114.4.a.b	$114$	$4$	114.a	1.a	$1$	$1$	$1$	$6.726$	$\Q$	None	✓	$1$	$1$	$-2$	$3$	$-7$	$-15$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-7q^{5}-6q^{6}+\cdots$
114.4.a.c	$114$	$4$	114.a	1.a	$1$	$1$	$1$	$6.726$	$\Q$	None	✓	$1$	$0$	$-2$	$3$	$12$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+12q^{5}-6q^{6}+\cdots$
114.4.a.d	$114$	$4$	114.a	1.a	$1$	$1$	$1$	$6.726$	$\Q$	None	✓	$1$	$1$	$2$	$-3$	$-11$	$-15$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-11q^{5}-6q^{6}+\cdots$
114.4.a.e	$114$	$4$	114.a	1.a	$1$	$2$	$2$	$6.726$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$4$	$-6$	$18$	$4$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(9+\beta )q^{5}-6q^{6}+\cdots$
114.4.a.f	$114$	$4$	114.a	1.a	$1$	$2$	$2$	$6.726$	$\Q(\sqrt{273}) $	None	✓	$1$	$0$	$4$	$6$	$11$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(6-\beta )q^{5}+6q^{6}+\cdots$
114.4.b.a	$114$	$4$	114.b	57.d	$2$	$10$	$10$	$6.726$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-20$	$5$	$0$	$10$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
114.4.b.b	$114$	$4$	114.b	57.d	$2$	$10$	$10$	$6.726$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$20$	$-5$	$0$	$10$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}-\beta _{3}q^{3}+4q^{4}+(\beta _{3}+\beta _{4})q^{5}+\cdots$
114.4.e.a	$114$	$4$	114.e	19.c	$3$	$2$	$1$	$6.726$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$2$	$-3$	$-2$	$-42$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
114.4.e.b	$114$	$4$	114.e	19.c	$3$	$2$	$1$	$6.726$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-3$	$6$	$38$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
114.4.e.c	$114$	$4$	114.e	19.c	$3$	$4$	$2$	$6.726$	$\Q(\sqrt{-3}, \sqrt{-10})$	None		$2$	$0$	$-4$	$-6$	$-8$	$36$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-2\beta _{1}q^{2}-3\beta _{1}q^{3}+(-4+4\beta _{1})q^{4}+\cdots$
114.4.e.d	$114$	$4$	114.e	19.c	$3$	$6$	$3$	$6.726$	6.0.627014547.1	None		$2$	$0$	$-6$	$9$	$-10$	$14$		$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-2\beta _{1}q^{2}+3\beta _{1}q^{3}+(-4+4\beta _{1})q^{4}+\cdots$
114.4.e.e	$114$	$4$	114.e	19.c	$3$	$6$	$3$	$6.726$	6.0.6967728.1	None		$2$	$0$	$6$	$9$	$-2$	$-34$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2+2\beta _{3})q^{2}+(3+3\beta _{3})q^{3}+4\beta _{3}q^{4}+\cdots$
114.4.h.a	$114$	$4$	114.h	57.f	$6$	$20$	$10$	$6.726$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-20$	$-4$	$0$	$-10$		$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2-2\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots$
114.4.h.b	$114$	$4$	114.h	57.f	$6$	$20$	$10$	$6.726$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$20$	$1$	$0$	$-10$		$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q-2\beta _{1}q^{2}-\beta _{5}q^{3}+(-4-4\beta _{1})q^{4}+\cdots$
114.4.i.a	$114$	$4$	114.i	19.e	$9$	$12$	$2$	$6.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$-15$	$42$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-2\beta _{3}-2\beta _{8})q^{2}-3\beta _{3}q^{3}-4\beta _{5}q^{4}+\cdots$
114.4.i.b	$114$	$4$	114.i	19.e	$9$	$12$	$2$	$6.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$-9$	$12$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(2\beta _{4}-2\beta _{7})q^{2}-3\beta _{4}q^{3}-4\beta _{8}q^{4}+\cdots$
114.4.i.c	$114$	$4$	114.i	19.e	$9$	$18$	$3$	$6.726$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$0$	$0$	$9$	$-30$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-2\beta _{4}+2\beta _{6})q^{2}-3\beta _{4}q^{3}+(4\beta _{5}+\cdots)q^{4}+\cdots$
114.4.i.d	$114$	$4$	114.i	19.e	$9$	$18$	$3$	$6.726$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$0$	$0$	$15$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{9}]$	$q+2\beta _{5}q^{2}-3\beta _{6}q^{3}+4\beta _{7}q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots$
114.4.l.a	$114$	$4$	114.l	57.j	$18$	$60$	$10$	$6.726$		None		$2$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
114.4.l.b	$114$	$4$	114.l	57.j	$18$	$60$	$10$	$6.726$		None		$2$	$0$	$0$	$9$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$

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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.