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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 86 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
615.1.h.a	$615$	$1$	615.h	615.h	$2$	$2$	$2$	$0.307$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-615}) $	None	✓	✓			615.1.h.a	$2$	$0$	$-1$	$-2$	$2$	$1$		$1$		$q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}+q^{5}+\cdots$
615.1.h.b	$615$	$1$	615.h	615.h	$2$	$2$	$2$	$0.307$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-615}) $	None	✓	✓			615.1.h.a	$2$	$0$	$-1$	$2$	$2$	$-1$		$1$		$q-\beta q^{2}+q^{3}+\beta q^{4}+q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
615.1.h.c	$615$	$1$	615.h	615.h	$2$	$2$	$2$	$0.307$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-615}) $	None	✓	✓			615.1.h.a	$2$	$0$	$1$	$-2$	$-2$	$1$		$1$		$q+\beta q^{2}-q^{3}+\beta q^{4}-q^{5}-\beta q^{6}+\beta q^{7}+\cdots$
615.1.h.d	$615$	$1$	615.h	615.h	$2$	$2$	$2$	$0.307$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-615}) $	None	✓	✓			615.1.h.a	$2$	$0$	$1$	$2$	$-2$	$-1$		$1$		$q+(1-\beta )q^{2}+q^{3}+(1-\beta )q^{4}-q^{5}+\cdots$
615.2.a.a	$615$	$2$	615.a	1.a	$1$	$1$	$1$	$4.911$	$\Q$	$_{}$	None	None	✓	✓			615.2.a.a	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots$
615.2.a.b	$615$	$2$	615.a	1.a	$1$	$1$	$1$	$4.911$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	615.2.a.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}-2q^{12}+\cdots$
615.2.a.c	$615$	$2$	615.a	1.a	$1$	$2$	$2$	$4.911$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		615.2.a.c	$1$	$1$	$-1$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots$
615.2.a.d	$615$	$2$	615.a	1.a	$1$	$4$	$4$	$4.911$	4.4.3981.1	$_{}$	None	None	✓	✓	✓	✓	615.2.a.d	$1$	$0$	$3$	$-4$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
615.2.a.e	$615$	$2$	615.a	1.a	$1$	$5$	$5$	$4.911$	5.5.1122797.1	$_{}$	None	None	✓	✓	✓	✓	615.2.a.e	$1$	$0$	$1$	$-5$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
615.2.a.f	$615$	$2$	615.a	1.a	$1$	$6$	$6$	$4.911$	6.6.69796620.1	$_{}$	None	None	✓	✓	✓	✓	615.2.a.f	$1$	$0$	$1$	$6$	$-6$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
615.2.a.g	$615$	$2$	615.a	1.a	$1$	$8$	$8$	$4.911$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	615.2.a.g	$1$	$0$	$2$	$8$	$8$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
615.2.b.a	$615$	$2$	615.b	5.b	$2$	$20$	$20$	$4.911$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			615.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{16}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
615.2.b.b	$615$	$2$	615.b	5.b	$2$	$20$	$20$	$4.911$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			615.2.b.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
615.2.e.a	$615$	$2$	615.e	205.c	$2$	$20$	$20$	$4.911$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			615.2.e.a	$2$	$0$	$0$	$-20$	$2$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
615.2.e.b	$615$	$2$	615.e	205.c	$2$	$20$	$20$	$4.911$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			615.2.e.a	$2$	$0$	$0$	$20$	$2$	$4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
615.2.f.a	$615$	$2$	615.f	41.b	$2$	$2$	$2$	$4.911$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			615.2.f.a	$2$	$0$	$-2$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+i q^{3}-q^{4}-q^{5}-i q^{6}+\cdots$
615.2.f.b	$615$	$2$	615.f	41.b	$2$	$12$	$12$	$4.911$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			615.2.f.b	$2$	$0$	$4$	$0$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-\beta _{5}q^{3}+(1-\beta _{2})q^{4}-q^{5}+\cdots$
615.2.f.c	$615$	$2$	615.f	41.b	$2$	$14$	$14$	$4.911$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓	✓		615.2.f.c	$2$	$0$	$-2$	$0$	$14$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(1-\beta _{2})q^{4}+q^{5}+\cdots$
615.2.j.a	$615$	$2$	615.j	41.c	$4$	$4$	$2$	$4.911$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			615.2.j.a	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}+(-1+\cdots)q^{4}+\cdots$
615.2.j.b	$615$	$2$	615.j	41.c	$4$	$4$	$2$	$4.911$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			615.2.j.b	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{5}+\cdots$
615.2.j.c	$615$	$2$	615.j	41.c	$4$	$20$	$10$	$4.911$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			615.2.j.c	$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
615.2.j.d	$615$	$2$	615.j	41.c	$4$	$28$	$14$	$4.911$		$_{}$	None	None		✓	✓		615.2.j.d	$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
615.2.k.a	$615$	$2$	615.k	615.k	$4$	$160$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.k.a	$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
615.2.m.a	$615$	$2$	615.m	15.e	$4$	$4$	$2$	$4.911$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			615.2.m.a	$2$	$1$	$-2$	$0$	$-8$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{3} q^{2}+(\beta_{3}-\beta_1+1)q^{3}+(-\beta_{3}+\beta_1-1)q^{4}+\cdots$
615.2.m.b	$615$	$2$	615.m	15.e	$4$	$4$	$2$	$4.911$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			615.2.m.a	$2$	$0$	$2$	$0$	$8$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{2}-\beta_1+1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots$
615.2.m.c	$615$	$2$	615.m	15.e	$4$	$76$	$38$	$4.911$		$_{}$	None	None		✓			615.2.m.c	$2$	$0$	$-2$	$-2$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
615.2.m.d	$615$	$2$	615.m	15.e	$4$	$76$	$38$	$4.911$		$_{}$	None	None		✓			615.2.m.c	$2$	$0$	$2$	$-2$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
615.2.p.a	$615$	$2$	615.p	615.p	$4$	$160$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.p.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
615.2.r.a	$615$	$2$	615.r	615.r	$4$	$160$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.k.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
615.2.s.a	$615$	$2$	615.s	205.j	$4$	$88$	$44$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.s.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
615.2.u.a	$615$	$2$	615.u	41.d	$5$	$28$	$7$	$4.911$		$_{}$	None	None		✓			615.2.u.a	$2$	$0$	$-1$	$-28$	$7$	$5$			$\mathrm{SU}(2)[C_{5}]$
615.2.u.b	$615$	$2$	615.u	41.d	$5$	$28$	$7$	$4.911$		$_{}$	None	None		✓			615.2.u.b	$2$	$0$	$-1$	$28$	$7$	$-3$			$\mathrm{SU}(2)[C_{5}]$
615.2.u.c	$615$	$2$	615.u	41.d	$5$	$28$	$7$	$4.911$		$_{}$	None	None		✓			615.2.u.c	$2$	$0$	$1$	$-28$	$-7$	$-5$			$\mathrm{SU}(2)[C_{5}]$
615.2.u.d	$615$	$2$	615.u	41.d	$5$	$28$	$7$	$4.911$		$_{}$	None	None		✓			615.2.u.d	$2$	$0$	$1$	$28$	$-7$	$3$			$\mathrm{SU}(2)[C_{5}]$
615.2.w.a	$615$	$2$	615.w	205.l	$8$	$168$	$42$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.w.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
615.2.x.a	$615$	$2$	615.x	615.x	$8$	$320$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.x.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
615.2.ba.a	$615$	$2$	615.ba	123.i	$8$	$112$	$28$	$4.911$		$_{}$	None	None		✓			615.2.ba.a	$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
615.2.ba.b	$615$	$2$	615.ba	123.i	$8$	$112$	$28$	$4.911$		$_{}$	None	None		✓			615.2.ba.a	$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
615.2.bb.a	$615$	$2$	615.bb	205.o	$8$	$168$	$42$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.w.a	$2$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
615.2.bf.a	$615$	$2$	615.bf	41.f	$10$	$8$	$2$	$4.911$	$\Q(\zeta_{20})$	$_{}$	None	None		✓			615.2.bf.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}-\zeta_{20}^{5}q^{3}+(\zeta_{20}^{2}+\cdots)q^{4}+\cdots$
615.2.bf.b	$615$	$2$	615.bf	41.f	$10$	$48$	$12$	$4.911$		$_{}$	None	None		✓			615.2.bf.b	$2$	$0$	$-2$	$0$	$12$	$-10$			$\mathrm{SU}(2)[C_{10}]$
615.2.bf.c	$615$	$2$	615.bf	41.f	$10$	$56$	$14$	$4.911$		$_{}$	None	None		✓	✓		615.2.bf.c	$2$	$0$	$2$	$0$	$-14$	$10$			$\mathrm{SU}(2)[C_{10}]$
615.2.bg.a	$615$	$2$	615.bg	205.r	$10$	$80$	$20$	$4.911$		$_{}$	None	None		✓			615.2.bg.a	$2$	$0$	$0$	$-80$	$3$	$4$			$\mathrm{SU}(2)[C_{10}]$
615.2.bg.b	$615$	$2$	615.bg	205.r	$10$	$80$	$20$	$4.911$		$_{}$	None	None		✓			615.2.bg.a	$2$	$0$	$0$	$80$	$-7$	$-4$			$\mathrm{SU}(2)[C_{10}]$
615.2.bj.a	$615$	$2$	615.bj	205.q	$10$	$160$	$40$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.bj.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{10}]$
615.2.bl.a	$615$	$2$	615.bl	205.s	$20$	$352$	$44$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.bl.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
615.2.bm.a	$615$	$2$	615.bm	615.am	$20$	$640$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.bm.a	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{20}]$
615.2.bo.a	$615$	$2$	615.bo	615.ao	$20$	$640$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.bo.a	$8$	$0$	$0$	$0$	$0$	$-20$			$\mathrm{SU}(2)[C_{20}]$
615.2.br.a	$615$	$2$	615.br	615.ar	$20$	$640$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.br.a	$8$	$0$	$0$	$-16$	$0$	$-12$			$\mathrm{SU}(2)[C_{20}]$
615.2.bt.a	$615$	$2$	615.bt	615.at	$20$	$640$	$80$	$4.911$		$_{}$	None	None		✓	✓	✓	615.2.bm.a	$4$	$0$	$0$	$-16$	$0$	$-20$			$\mathrm{SU}(2)[C_{20}]$

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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.