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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

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Results (1-50 of 133 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
231.1.h.a	$231$	$1$	231.h	231.h	$2$	$1$	$1$	$0.115$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$-1$		$1$		$q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots$
231.1.h.b	$231$	$1$	231.h	231.h	$2$	$1$	$1$	$0.115$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$-1$	$1$	$-1$	$1$		$1$		$q-q^{2}+q^{3}-q^{5}-q^{6}+q^{7}+q^{8}+\cdots$
231.1.h.c	$231$	$1$	231.h	231.h	$2$	$1$	$1$	$0.115$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$1$	$-1$	$1$	$1$		$1$		$q+q^{2}-q^{3}+q^{5}-q^{6}+q^{7}-q^{8}+\cdots$
231.1.h.d	$231$	$1$	231.h	231.h	$2$	$1$	$1$	$0.115$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$1$	$1$	$-1$	$-1$		$1$		$q+q^{2}+q^{3}-q^{5}+q^{6}-q^{7}-q^{8}+\cdots$
231.2.a.a	$231$	$2$	231.a	1.a	$1$	$1$	$1$	$1.845$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
231.2.a.b	$231$	$2$	231.a	1.a	$1$	$2$	$2$	$1.845$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$-2$	$6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}+\beta q^{6}+\cdots$
231.2.a.c	$231$	$2$	231.a	1.a	$1$	$2$	$2$	$1.845$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
231.2.a.d	$231$	$2$	231.a	1.a	$1$	$3$	$3$	$1.845$	3.3.837.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
231.2.a.e	$231$	$2$	231.a	1.a	$1$	$3$	$3$	$1.845$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$2$	$3$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+(1+\cdots)q^{5}+\cdots$
231.2.c.a	$231$	$2$	231.c	77.b	$2$	$16$	$16$	$1.845$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
231.2.e.a	$231$	$2$	231.e	21.c	$2$	$28$	$28$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
231.2.g.a	$231$	$2$	231.g	33.d	$2$	$24$	$24$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
231.2.i.a	$231$	$2$	231.i	7.c	$3$	$2$	$1$	$1.845$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$1$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
231.2.i.b	$231$	$2$	231.i	7.c	$3$	$2$	$1$	$1.845$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$1$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
231.2.i.c	$231$	$2$	231.i	7.c	$3$	$2$	$1$	$1.845$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$1$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
231.2.i.d	$231$	$2$	231.i	7.c	$3$	$4$	$2$	$1.845$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$2$	$-2$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
231.2.i.e	$231$	$2$	231.i	7.c	$3$	$8$	$4$	$1.845$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$-4$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
231.2.i.f	$231$	$2$	231.i	7.c	$3$	$10$	$5$	$1.845$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$5$	$4$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots$
231.2.j.a	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-4$	$1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
231.2.j.b	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-2$	$1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$
231.2.j.c	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$1$	$1$	$7$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
231.2.j.d	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$-1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$
231.2.j.e	$231$	$2$	231.j	11.c	$5$	$4$	$1$	$1.845$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$5$	$1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
231.2.j.f	$231$	$2$	231.j	11.c	$5$	$8$	$2$	$1.845$	8.0.13140625.1	$_{}$	None	None		$2$	$0$	$2$	$2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
231.2.j.g	$231$	$2$	231.j	11.c	$5$	$20$	$5$	$1.845$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-5$	$-5$	$5$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}-\beta _{4}q^{3}+(\beta _{3}-\beta _{6}-\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots$
231.2.l.a	$231$	$2$	231.l	231.l	$6$	$8$	$4$	$1.845$	8.0.$\cdots$.5	$_{}$	None	None		$8$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}+\beta _{4})q^{3}+2\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots$
231.2.l.b	$231$	$2$	231.l	231.l	$6$	$48$	$24$	$1.845$		$_{}$	None	None		$8$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
231.2.n.a	$231$	$2$	231.n	21.g	$6$	$52$	$26$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{6}]$
231.2.p.a	$231$	$2$	231.p	77.i	$6$	$32$	$16$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
231.2.s.a	$231$	$2$	231.s	33.f	$10$	$96$	$24$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$6$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
231.2.u.a	$231$	$2$	231.u	231.u	$10$	$112$	$28$	$1.845$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{10}]$
231.2.w.a	$231$	$2$	231.w	77.l	$10$	$64$	$16$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$10$			$\mathrm{SU}(2)[C_{10}]$
231.2.y.a	$231$	$2$	231.y	77.m	$15$	$64$	$8$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$-1$			$\mathrm{SU}(2)[C_{15}]$
231.2.y.b	$231$	$2$	231.y	77.m	$15$	$64$	$8$	$1.845$		$_{}$	None	None		$4$	$0$	$4$	$8$	$-4$	$-1$			$\mathrm{SU}(2)[C_{15}]$
231.2.ba.a	$231$	$2$	231.ba	77.n	$30$	$128$	$16$	$1.845$		$_{}$	None	None		$4$	$0$	$0$	$0$	$12$	$-10$			$\mathrm{SU}(2)[C_{30}]$
231.2.bc.a	$231$	$2$	231.bc	231.ac	$30$	$224$	$28$	$1.845$		$_{}$	None	None		$8$	$0$	$0$	$-9$	$0$	$-16$			$\mathrm{SU}(2)[C_{30}]$
231.2.be.a	$231$	$2$	231.be	231.ae	$30$	$224$	$28$	$1.845$		$_{}$	None	None		$8$	$0$	$0$	$-3$	$0$	$-20$			$\mathrm{SU}(2)[C_{30}]$
231.3.b.a	$231$	$3$	231.b	3.b	$2$	$40$	$40$	$6.294$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
231.3.d.a	$231$	$3$	231.d	11.b	$2$	$24$	$24$	$6.294$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
231.3.f.a	$231$	$3$	231.f	7.b	$2$	$28$	$28$	$6.294$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
231.3.h.a	$231$	$3$	231.h	231.h	$2$	$3$	$3$	$6.294$	3.3.6237.1	$_{}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$-9$	$0$	$-21$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots$
231.3.h.b	$231$	$3$	231.h	231.h	$2$	$3$	$3$	$6.294$	3.3.6237.1	$_{}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$-9$	$0$	$21$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots$
231.3.h.c	$231$	$3$	231.h	231.h	$2$	$3$	$3$	$6.294$	3.3.6237.1	$_{}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$9$	$0$	$-21$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots$
231.3.h.d	$231$	$3$	231.h	231.h	$2$	$3$	$3$	$6.294$	3.3.6237.1	$_{}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$9$	$0$	$21$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots$
231.3.h.e	$231$	$3$	231.h	231.h	$2$	$48$	$48$	$6.294$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
231.3.k.a	$231$	$3$	231.k	231.k	$6$	$120$	$60$	$6.294$		$_{}$	None	None		$8$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
231.3.m.a	$231$	$3$	231.m	7.d	$6$	$24$	$12$	$6.294$		$_{}$	None	None		$2$	$0$	$0$	$-36$	$0$	$-10$			$\mathrm{SU}(2)[C_{6}]$
231.3.m.b	$231$	$3$	231.m	7.d	$6$	$28$	$14$	$6.294$		$_{}$	None	None		$2$	$0$	$0$	$42$	$0$	$16$			$\mathrm{SU}(2)[C_{6}]$
231.3.o.a	$231$	$3$	231.o	77.h	$6$	$64$	$32$	$6.294$		$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{6}]$
231.3.q.a	$231$	$3$	231.q	21.h	$6$	$108$	$54$	$6.294$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$

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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.