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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 (48 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
979.1.b.a	$979$	$1$	979.b	979.b	$2$	$1$	$1$	$0.489$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-979}) $	$\Q(\sqrt{89}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+q^{4}-2q^{5}+q^{9}+q^{11}+q^{16}-2q^{20}+\cdots$
979.1.b.b	$979$	$1$	979.b	979.b	$2$	$2$	$2$	$0.489$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-979}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-\beta q^{7}+q^{9}-q^{11}+\beta q^{13}+\cdots$
979.1.e.a	$979$	$1$	979.e	979.e	$4$	$2$	$1$	$0.489$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-1-i)q^{3}+q^{4}-iq^{5}+iq^{9}+\cdots$
979.1.q.a	$979$	$1$	979.q	979.q	$22$	$10$	$1$	$0.489$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$9$	$-2$	$0$		$1$		$q+(1-\zeta_{22}^{5})q^{3}-\zeta_{22}^{3}q^{4}+(\zeta_{22}^{2}+\cdots)q^{5}+\cdots$
979.1.r.a	$979$	$1$	979.r	979.r	$22$	$10$	$1$	$0.489$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-11$	$2$	$0$		$1$		$q+(-1-\zeta_{22}^{5})q^{3}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}^{2}+\cdots)q^{5}+\cdots$
979.1.v.a	$979$	$1$	979.v	979.v	$44$	$20$	$1$	$0.489$	$\Q(\zeta_{44})$	$D_{44}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\zeta_{44}^{11}-\zeta_{44}^{20})q^{3}+\zeta_{44}^{12}q^{4}+\cdots$
979.2.a.a	$979$	$2$	979.a	1.a	$1$	$1$	$1$	$7.817$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}+3q^{5}+q^{9}-q^{11}+\cdots$
979.2.a.b	$979$	$2$	979.a	1.a	$1$	$1$	$1$	$7.817$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}-q^{4}-2q^{5}+2q^{6}-2q^{7}+\cdots$
979.2.a.c	$979$	$2$	979.a	1.a	$1$	$11$	$11$	$7.817$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$-10$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
979.2.a.d	$979$	$2$	979.a	1.a	$1$	$17$	$17$	$7.817$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-1$	$-14$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
979.2.a.e	$979$	$2$	979.a	1.a	$1$	$18$	$18$	$7.817$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$-1$	$11$	$3$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{12}+\cdots)q^{5}+\cdots$
979.2.a.f	$979$	$2$	979.a	1.a	$1$	$25$	$25$	$7.817$		$_{}$	None	None	✓	$1$	$0$	$4$	$3$	$18$	$-1$	$-$		$\mathrm{SU}(2)$
979.2.d.a	$979$	$2$	979.d	89.b	$2$	$4$	$4$	$7.817$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+q^{4}+3q^{5}+(-2\beta _{1}+\cdots)q^{6}+\cdots$
979.2.d.b	$979$	$2$	979.d	89.b	$2$	$32$	$32$	$7.817$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
979.2.d.c	$979$	$2$	979.d	89.b	$2$	$40$	$40$	$7.817$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{2}]$
979.2.f.a	$979$	$2$	979.f	89.c	$4$	$2$	$1$	$7.817$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(1+i)q^{3}-q^{4}+4iq^{5}+(1+\cdots)q^{6}+\cdots$
979.2.f.b	$979$	$2$	979.f	89.c	$4$	$70$	$35$	$7.817$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{4}]$
979.2.f.c	$979$	$2$	979.f	89.c	$4$	$76$	$38$	$7.817$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
979.2.g.a	$979$	$2$	979.g	11.c	$5$	$4$	$1$	$7.817$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$-1$	$-2$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\cdots$
979.2.g.b	$979$	$2$	979.g	11.c	$5$	$172$	$43$	$7.817$		$_{}$	None	None		$2$	$0$	$-5$	$2$	$1$	$-27$			$\mathrm{SU}(2)[C_{5}]$
979.2.g.c	$979$	$2$	979.g	11.c	$5$	$176$	$44$	$7.817$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$19$			$\mathrm{SU}(2)[C_{5}]$
979.2.h.a	$979$	$2$	979.h	979.h	$8$	$8$	$2$	$7.817$	8.0.959512576.1	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(\beta _{5}-\beta _{6}-\beta _{7})q^{3}+2q^{4}+3\beta _{5}q^{5}+\cdots$
979.2.h.b	$979$	$2$	979.h	979.h	$8$	$344$	$86$	$7.817$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{8}]$
979.2.j.a	$979$	$2$	979.j	979.j	$10$	$8$	$2$	$7.817$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$10$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2\zeta_{20}^{2}-\zeta_{20}^{4}+2\zeta_{20}^{6})q^{2}-\zeta_{20}^{7}q^{3}+\cdots$
979.2.j.b	$979$	$2$	979.j	979.j	$10$	$344$	$86$	$7.817$		$_{}$	None	None		$4$	$0$	$-14$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{10}]$
979.2.m.a	$979$	$2$	979.m	89.e	$11$	$360$	$36$	$7.817$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{11}]$
979.2.m.b	$979$	$2$	979.m	89.e	$11$	$400$	$40$	$7.817$		$_{}$	None	None		$2$	$0$	$-2$	$9$	$-14$	$-2$			$\mathrm{SU}(2)[C_{11}]$
979.2.n.a	$979$	$2$	979.n	979.n	$20$	$704$	$88$	$7.817$		$_{}$	None	None		$4$	$0$	$-16$	$-4$	$0$	$-6$			$\mathrm{SU}(2)[C_{20}]$
979.2.p.a	$979$	$2$	979.p	89.f	$22$	$360$	$36$	$7.817$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{22}]$
979.2.p.b	$979$	$2$	979.p	89.f	$22$	$400$	$40$	$7.817$		$_{}$	None	None		$2$	$0$	$0$	$-11$	$6$	$0$			$\mathrm{SU}(2)[C_{22}]$
979.2.t.a	$979$	$2$	979.t	979.t	$40$	$1408$	$88$	$7.817$		$_{}$	None	None		$4$	$0$	$-40$	$-20$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
979.2.u.a	$979$	$2$	979.u	89.g	$44$	$700$	$35$	$7.817$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{44}]$
979.2.u.b	$979$	$2$	979.u	89.g	$44$	$780$	$39$	$7.817$		$_{}$	None	None		$2$	$0$	$-2$	$2$	$0$	$-2$			$\mathrm{SU}(2)[C_{44}]$
979.2.w.a	$979$	$2$	979.w	979.w	$55$	$3520$	$88$	$7.817$		$_{}$	None	None		$4$	$0$	$-29$	$-22$	$-29$	$-27$			$\mathrm{SU}(2)[C_{55}]$
979.2.y.a	$979$	$2$	979.y	979.y	$88$	$40$	$1$	$7.817$		$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{88}]$
979.2.y.b	$979$	$2$	979.y	979.y	$88$	$40$	$1$	$7.817$		$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{88}]$
979.2.y.c	$979$	$2$	979.y	979.y	$88$	$3440$	$86$	$7.817$		$_{}$	None	None		$4$	$0$	$0$	$-88$	$-80$	$0$			$\mathrm{SU}(2)[C_{88}]$
979.2.bb.a	$979$	$2$	979.bb	979.ab	$110$	$3520$	$88$	$7.817$		$_{}$	None	None		$4$	$0$	$-29$	$-44$	$-25$	$-33$			$\mathrm{SU}(2)[C_{110}]$
979.2.bd.a	$979$	$2$	979.bd	979.ad	$220$	$7040$	$88$	$7.817$		$_{}$	None	None		$4$	$0$	$-50$	$-62$	$-66$	$-60$			$\mathrm{SU}(2)[C_{220}]$
979.2.be.a	$979$	$2$	979.be	979.ae	$440$	$14080$	$88$	$7.817$		$_{}$	None	None		$4$	$0$	$-180$	$-112$	$-120$	$-200$			$\mathrm{SU}(2)[C_{440}]$
979.4.a.a	$979$	$4$	979.a	1.a	$1$	$48$	$48$	$57.763$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-12$	$-90$	$-24$	$-$		$\mathrm{SU}(2)$
979.4.a.b	$979$	$4$	979.a	1.a	$1$	$54$	$54$	$57.763$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-6$	$-70$	$-52$	$-$		$\mathrm{SU}(2)$
979.4.a.c	$979$	$4$	979.a	1.a	$1$	$56$	$56$	$57.763$		$_{}$	None	None	✓	$1$	$0$	$8$	$0$	$70$	$4$	$+$		$\mathrm{SU}(2)$
979.4.a.d	$979$	$4$	979.a	1.a	$1$	$62$	$62$	$57.763$		$_{}$	None	None	✓	$1$	$0$	$8$	$18$	$90$	$32$	$+$		$\mathrm{SU}(2)$
979.6.a.a	$979$	$6$	979.a	1.a	$1$	$85$	$85$	$157.016$		$_{}$	None	None	✓	$1$	$1$	$-16$	$-63$	$-450$	$-341$	$+$		$\mathrm{SU}(2)$
979.6.a.b	$979$	$6$	979.a	1.a	$1$	$91$	$91$	$157.016$		$_{}$	None	None	✓	$1$	$1$	$-16$	$-9$	$-350$	$-145$	$+$		$\mathrm{SU}(2)$
979.6.a.c	$979$	$6$	979.a	1.a	$1$	$93$	$93$	$157.016$		$_{}$	None	None	✓	$1$	$0$	$16$	$9$	$350$	$247$	$-$		$\mathrm{SU}(2)$
979.6.a.d	$979$	$6$	979.a	1.a	$1$	$99$	$99$	$157.016$		$_{}$	None	None	✓	$1$	$0$	$16$	$27$	$450$	$51$	$-$		$\mathrm{SU}(2)$

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