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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 85 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
1968.1.b.a	$1968$	$1$	1968.b	123.b	$2$	$1$	$1$	$0.982$	$\Q$	$D_{3}$	$\Q(\sqrt{-123}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{9}+q^{11}-q^{17}+q^{25}-q^{27}+\cdots$
1968.1.b.b	$1968$	$1$	1968.b	123.b	$2$	$1$	$1$	$0.982$	$\Q$	$D_{3}$	$\Q(\sqrt{-123}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{9}-q^{11}+q^{17}+q^{25}+q^{27}+\cdots$
1968.1.z.a	$1968$	$1$	1968.z	1968.z	$4$	$4$	$2$	$0.982$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
1968.1.be.a	$1968$	$1$	1968.be	1968.ae	$4$	$4$	$2$	$0.982$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$4$		$1$		$q-\zeta_{8}q^{2}-q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
1968.2.a.a	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+2q^{7}+q^{9}+3q^{11}+\cdots$
1968.2.a.b	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
1968.2.a.c	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
1968.2.a.d	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}+5q^{11}+\cdots$
1968.2.a.e	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+3q^{11}-6q^{13}+\cdots$
1968.2.a.f	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$
1968.2.a.g	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots$
1968.2.a.h	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots$
1968.2.a.i	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$
1968.2.a.j	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+4q^{7}+q^{9}-5q^{11}+\cdots$
1968.2.a.k	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots$
1968.2.a.l	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
1968.2.a.m	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-7q^{13}+\cdots$
1968.2.a.n	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-4q^{7}+q^{9}-5q^{11}+\cdots$
1968.2.a.o	$1968$	$2$	1968.a	1.a	$1$	$1$	$1$	$15.715$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
1968.2.a.p	$1968$	$2$	1968.a	1.a	$1$	$2$	$2$	$15.715$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots$
1968.2.a.q	$1968$	$2$	1968.a	1.a	$1$	$2$	$2$	$15.715$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+(-1-\beta )q^{7}+q^{9}+\cdots$
1968.2.a.r	$1968$	$2$	1968.a	1.a	$1$	$2$	$2$	$15.715$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots$
1968.2.a.s	$1968$	$2$	1968.a	1.a	$1$	$2$	$2$	$15.715$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+(-2-\beta )q^{7}+\cdots$
1968.2.a.t	$1968$	$2$	1968.a	1.a	$1$	$3$	$3$	$15.715$	3.3.961.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$1$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}-2q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
1968.2.a.u	$1968$	$2$	1968.a	1.a	$1$	$3$	$3$	$15.715$	3.3.892.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{2}q^{5}-\beta _{2}q^{7}+q^{9}+(3-\beta _{1}+\cdots)q^{11}+\cdots$
1968.2.a.v	$1968$	$2$	1968.a	1.a	$1$	$3$	$3$	$15.715$	3.3.1436.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots$
1968.2.a.w	$1968$	$2$	1968.a	1.a	$1$	$3$	$3$	$15.715$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1968.2.a.x	$1968$	$2$	1968.a	1.a	$1$	$5$	$5$	$15.715$	5.5.3858104.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-5$	$1$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{4}q^{5}-\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
1968.2.d.a	$1968$	$2$	1968.d	12.b	$2$	$4$	$4$	$15.715$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}^{2}q^{3}+3\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots$
1968.2.d.b	$1968$	$2$	1968.d	12.b	$2$	$28$	$28$	$15.715$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1968.2.d.c	$1968$	$2$	1968.d	12.b	$2$	$48$	$48$	$15.715$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1968.2.g.a	$1968$	$2$	1968.g	492.d	$2$	$4$	$4$	$15.715$	$\Q(\sqrt{-3}, \sqrt{41})$	$_{}$	$\Q(\sqrt{-123}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-3q^{9}+\beta _{2}q^{11}+(-5+\beta _{3})q^{17}+\cdots$
1968.2.g.b	$1968$	$2$	1968.g	492.d	$2$	$4$	$4$	$15.715$	$\Q(\sqrt{-3}, \sqrt{41})$	$_{}$	$\Q(\sqrt{-123}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-3q^{9}-\beta _{1}q^{11}-\beta _{2}q^{17}+\cdots$
1968.2.g.c	$1968$	$2$	1968.g	492.d	$2$	$4$	$4$	$15.715$	$\Q(\sqrt{-3}, \sqrt{41})$	$_{}$	$\Q(\sqrt{-123}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}-3q^{9}-\beta _{2}q^{11}+(5-\beta _{3})q^{17}+\cdots$
1968.2.g.d	$1968$	$2$	1968.g	492.d	$2$	$8$	$8$	$15.715$	8.0.$\cdots$.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{3}+\beta _{5}q^{5}-\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots$
1968.2.g.e	$1968$	$2$	1968.g	492.d	$2$	$16$	$16$	$15.715$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-41}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{10}q^{7}+\beta _{2}q^{9}+\cdots$
1968.2.g.f	$1968$	$2$	1968.g	492.d	$2$	$16$	$16$	$15.715$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}+\beta _{10}q^{5}+(\beta _{6}+\beta _{7}+\beta _{9}+\cdots)q^{7}+\cdots$
1968.2.g.g	$1968$	$2$	1968.g	492.d	$2$	$32$	$32$	$15.715$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1968.2.j.a	$1968$	$2$	1968.j	41.b	$2$	$2$	$2$	$15.715$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}-2q^{5}-2iq^{7}-q^{9}+4iq^{11}+\cdots$
1968.2.j.b	$1968$	$2$	1968.j	41.b	$2$	$2$	$2$	$15.715$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+q^{5}+2iq^{7}-q^{9}+iq^{13}+\cdots$
1968.2.j.c	$1968$	$2$	1968.j	41.b	$2$	$4$	$4$	$15.715$	$\Q(i, \sqrt{57})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(1-\beta _{3})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots$
1968.2.j.d	$1968$	$2$	1968.j	41.b	$2$	$6$	$6$	$15.715$	6.0.5089536.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(1+\beta _{1})q^{5}+(\beta _{2}-\beta _{5})q^{7}+\cdots$
1968.2.j.e	$1968$	$2$	1968.j	41.b	$2$	$8$	$8$	$15.715$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(-1-\beta _{6})q^{5}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
1968.2.j.f	$1968$	$2$	1968.j	41.b	$2$	$8$	$8$	$15.715$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$10$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(1+\beta _{4})q^{5}+(\beta _{1}+\beta _{7})q^{7}+\cdots$
1968.2.j.g	$1968$	$2$	1968.j	41.b	$2$	$12$	$12$	$15.715$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{10}q^{7}-q^{9}+\beta _{9}q^{11}+\cdots$
1968.2.t.a	$1968$	$2$	1968.t	41.c	$4$	$4$	$2$	$15.715$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+(2-2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
1968.2.t.b	$1968$	$2$	1968.t	41.c	$4$	$8$	$4$	$15.715$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
1968.2.t.c	$1968$	$2$	1968.t	41.c	$4$	$8$	$4$	$15.715$	8.0.4328587264.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{5}q^{3}+(\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1968.2.t.d	$1968$	$2$	1968.t	41.c	$4$	$12$	$6$	$15.715$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{3}+(\beta _{1}+\beta _{8}-\beta _{9})q^{5}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
1968.2.t.e	$1968$	$2$	1968.t	41.c	$4$	$16$	$8$	$15.715$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-12$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{3}+\beta _{10}q^{5}+(-1-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots$

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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.