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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 71 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
287.1.d.a	$287$	$1$	287.d	287.d	$2$	$3$	$3$	$0.143$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-287}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$3$		$1$		$q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
287.1.d.b	$287$	$1$	287.d	287.d	$2$	$3$	$3$	$0.143$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-287}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-3$		$1$		$q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
287.2.a.a	$287$	$2$	287.a	1.a	$1$	$2$	$2$	$2.292$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
287.2.a.b	$287$	$2$	287.a	1.a	$1$	$2$	$2$	$2.292$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
287.2.a.c	$287$	$2$	287.a	1.a	$1$	$3$	$3$	$2.292$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
287.2.a.d	$287$	$2$	287.a	1.a	$1$	$3$	$3$	$2.292$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$4$	$5$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(2-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
287.2.a.e	$287$	$2$	287.a	1.a	$1$	$5$	$5$	$2.292$	5.5.633117.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$-5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
287.2.a.f	$287$	$2$	287.a	1.a	$1$	$6$	$6$	$2.292$	6.6.185257757.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$-4$	$-1$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
287.2.c.a	$287$	$2$	287.c	41.b	$2$	$10$	$10$	$2.292$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$0$	$-10$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}-\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
287.2.c.b	$287$	$2$	287.c	41.b	$2$	$12$	$12$	$2.292$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{8})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
287.2.e.a	$287$	$2$	287.e	7.c	$3$	$4$	$2$	$2.292$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$-2$	$2$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
287.2.e.b	$287$	$2$	287.e	7.c	$3$	$4$	$2$	$2.292$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(2+2\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
287.2.e.c	$287$	$2$	287.e	7.c	$3$	$10$	$5$	$2.292$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$2$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{7}q^{2}+\beta _{8}q^{3}+(\beta _{1}-\beta _{2}-\beta _{6})q^{4}+\cdots$
287.2.e.d	$287$	$2$	287.e	7.c	$3$	$34$	$17$	$2.292$		$_{}$	None	None		$2$	$0$	$-3$	$-1$	$1$	$-2$			$\mathrm{SU}(2)[C_{3}]$
287.2.f.a	$287$	$2$	287.f	41.c	$4$	$40$	$20$	$2.292$		$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
287.2.h.a	$287$	$2$	287.h	41.d	$5$	$4$	$1$	$2.292$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+2\zeta_{10}^{3}q^{4}+\cdots$
287.2.h.b	$287$	$2$	287.h	41.d	$5$	$4$	$1$	$2.292$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$1$	$6$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
287.2.h.c	$287$	$2$	287.h	41.d	$5$	$40$	$10$	$2.292$		$_{}$	None	None		$2$	$0$	$-3$	$0$	$-4$	$-10$			$\mathrm{SU}(2)[C_{5}]$
287.2.h.d	$287$	$2$	287.h	41.d	$5$	$40$	$10$	$2.292$		$_{}$	None	None		$2$	$0$	$-2$	$-10$	$-1$	$10$			$\mathrm{SU}(2)[C_{5}]$
287.2.j.a	$287$	$2$	287.j	287.j	$6$	$52$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-2$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
287.2.l.a	$287$	$2$	287.l	287.l	$8$	$104$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-8$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
287.2.n.a	$287$	$2$	287.n	41.f	$10$	$88$	$22$	$2.292$		$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{10}]$
287.2.r.a	$287$	$2$	287.r	287.r	$12$	$4$	$1$	$2.292$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-6$	$10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
287.2.r.b	$287$	$2$	287.r	287.r	$12$	$4$	$1$	$2.292$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{12}q^{2}+(1+\zeta_{12})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
287.2.r.c	$287$	$2$	287.r	287.r	$12$	$96$	$24$	$2.292$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-14$			$\mathrm{SU}(2)[C_{12}]$
287.2.s.a	$287$	$2$	287.s	287.s	$15$	$208$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-3$	$-8$	$-7$	$-6$			$\mathrm{SU}(2)[C_{15}]$
287.2.u.a	$287$	$2$	287.u	41.g	$20$	$160$	$20$	$2.292$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
287.2.w.a	$287$	$2$	287.w	287.w	$24$	$208$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-4$	$-12$	$-12$	$-8$			$\mathrm{SU}(2)[C_{24}]$
287.2.z.a	$287$	$2$	287.z	287.z	$30$	$208$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-3$	$0$	$1$	$-10$			$\mathrm{SU}(2)[C_{30}]$
287.2.bb.a	$287$	$2$	287.bb	287.ab	$40$	$416$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-32$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{40}]$
287.2.bc.a	$287$	$2$	287.bc	287.ac	$60$	$416$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-10$	$-8$	$-10$	$-16$			$\mathrm{SU}(2)[C_{60}]$
287.2.be.a	$287$	$2$	287.be	287.ae	$120$	$832$	$26$	$2.292$		$_{}$	None	None		$4$	$0$	$-16$	$-48$	$-48$	$-32$			$\mathrm{SU}(2)[C_{120}]$
287.3.b.a	$287$	$3$	287.b	7.b	$2$	$52$	$52$	$7.820$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{2}]$
287.3.d.a	$287$	$3$	287.d	287.d	$2$	$7$	$7$	$7.820$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-287}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots$
287.3.d.b	$287$	$3$	287.d	287.d	$2$	$7$	$7$	$7.820$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-287}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-\beta _{4}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots$
287.3.d.c	$287$	$3$	287.d	287.d	$2$	$8$	$8$	$7.820$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$4$	$0$	$-8$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{4}q^{3}-3q^{4}+\beta _{6}q^{5}+\beta _{4}q^{6}+\cdots$
287.3.d.d	$287$	$3$	287.d	287.d	$2$	$32$	$32$	$7.820$		$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
287.3.g.a	$287$	$3$	287.g	287.g	$4$	$108$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{4}]$
287.3.i.a	$287$	$3$	287.i	287.i	$6$	$108$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-2$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
287.3.k.a	$287$	$3$	287.k	7.d	$6$	$108$	$54$	$7.820$		$_{}$	None	None		$2$	$0$	$-2$	$-6$	$-6$	$-4$			$\mathrm{SU}(2)[C_{6}]$
287.3.m.a	$287$	$3$	287.m	41.e	$8$	$168$	$42$	$7.820$		$_{}$	None	None		$2$	$0$	$8$	$-16$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
287.3.o.a	$287$	$3$	287.o	287.o	$10$	$216$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-6$	$0$	$0$	$-3$			$\mathrm{SU}(2)[C_{10}]$
287.3.p.a	$287$	$3$	287.p	287.p	$10$	$216$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-6$	$0$	$0$	$-5$			$\mathrm{SU}(2)[C_{10}]$
287.3.q.a	$287$	$3$	287.q	287.q	$12$	$216$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$
287.3.t.a	$287$	$3$	287.t	287.t	$20$	$432$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-20$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{20}]$
287.3.v.a	$287$	$3$	287.v	287.v	$24$	$432$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-4$	$-4$	$-4$	$-8$			$\mathrm{SU}(2)[C_{24}]$
287.3.x.a	$287$	$3$	287.x	287.x	$30$	$432$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-3$	$0$	$-9$	$-10$			$\mathrm{SU}(2)[C_{30}]$
287.3.y.a	$287$	$3$	287.y	287.y	$30$	$432$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-3$	$-24$	$-9$	$-6$			$\mathrm{SU}(2)[C_{30}]$
287.3.ba.a	$287$	$3$	287.ba	41.h	$40$	$672$	$42$	$7.820$		$_{}$	None	None		$2$	$0$	$-8$	$16$	$0$	$0$			$\mathrm{SU}(2)[C_{40}]$
287.3.bd.a	$287$	$3$	287.bd	287.ad	$60$	$864$	$54$	$7.820$		$_{}$	None	None		$4$	$0$	$-10$	$-24$	$-30$	$-16$			$\mathrm{SU}(2)[C_{60}]$

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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.