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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 202 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
756.1.d.a	$756$	$1$	756.d	7.b	$2$	$2$	$2$	$0.377$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$0$	$0$	$-2$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{17}+\cdots$
756.1.d.b	$756$	$1$	756.d	7.b	$2$	$2$	$2$	$0.377$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(\zeta_{6}+\cdots)q^{19}+\cdots$
756.1.h.a	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
756.1.h.b	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$1$		$1$		$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
756.1.h.c	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
756.1.h.d	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$		$1$		$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
756.1.z.a	$756$	$1$	756.z	7.d	$6$	$2$	$1$	$0.377$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}+(1-\zeta_{6}^{2})q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
756.1.bk.a	$756$	$1$	756.bk	21.h	$6$	$2$	$1$	$0.377$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{7}+q^{13}-\zeta_{6}^{2}q^{19}-\zeta_{6}q^{25}+\cdots$
756.2.a.a	$756$	$2$	756.a	1.a	$1$	$1$	$1$	$6.037$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}-3q^{11}+2q^{13}+6q^{17}+\cdots$
756.2.a.b	$756$	$2$	756.a	1.a	$1$	$1$	$1$	$6.037$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}+2q^{13}-3q^{17}-4q^{19}+\cdots$
756.2.a.c	$756$	$2$	756.a	1.a	$1$	$1$	$1$	$6.037$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-2q^{11}-5q^{17}+2q^{19}+\cdots$
756.2.a.d	$756$	$2$	756.a	1.a	$1$	$1$	$1$	$6.037$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+2q^{11}+5q^{17}+2q^{19}+\cdots$
756.2.a.e	$756$	$2$	756.a	1.a	$1$	$1$	$1$	$6.037$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+2q^{13}+3q^{17}-4q^{19}+\cdots$
756.2.a.f	$756$	$2$	756.a	1.a	$1$	$1$	$1$	$6.037$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+3q^{11}+2q^{13}-6q^{17}+\cdots$
756.2.a.g	$756$	$2$	756.a	1.a	$1$	$2$	$2$	$6.037$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{5}-q^{7}+\beta q^{11}+6q^{13}-2\beta q^{17}+\cdots$
756.2.b.a	$756$	$2$	756.b	28.d	$2$	$4$	$4$	$6.037$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots$
756.2.b.b	$756$	$2$	756.b	28.d	$2$	$4$	$4$	$6.037$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$
756.2.b.c	$756$	$2$	756.b	28.d	$2$	$12$	$12$	$6.037$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(1+\beta _{11})q^{4}-\beta _{8}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$
756.2.b.d	$756$	$2$	756.b	28.d	$2$	$12$	$12$	$6.037$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots$
756.2.b.e	$756$	$2$	756.b	28.d	$2$	$16$	$16$	$6.037$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{11}q^{5}+\beta _{6}q^{7}+\cdots$
756.2.b.f	$756$	$2$	756.b	28.d	$2$	$16$	$16$	$6.037$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{14}q^{2}+\beta _{8}q^{4}+\beta _{10}q^{5}+\beta _{6}q^{7}+\cdots$
756.2.e.a	$756$	$2$	756.e	12.b	$2$	$24$	$24$	$6.037$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
756.2.e.b	$756$	$2$	756.e	12.b	$2$	$24$	$24$	$6.037$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
756.2.f.a	$756$	$2$	756.f	21.c	$2$	$2$	$2$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-3q^{5}+(2-\zeta_{6})q^{7}+3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots$
756.2.f.b	$756$	$2$	756.f	21.c	$2$	$2$	$2$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-2-\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+(5+\cdots)q^{19}+\cdots$
756.2.f.c	$756$	$2$	756.f	21.c	$2$	$2$	$2$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+3q^{5}+(2-\zeta_{6})q^{7}-3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots$
756.2.f.d	$756$	$2$	756.f	21.c	$2$	$4$	$4$	$6.037$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots$
756.2.i.a	$756$	$2$	756.i	63.h	$3$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+4\zeta_{6}q^{11}+\cdots$
756.2.i.b	$756$	$2$	756.i	63.h	$3$	$14$	$7$	$6.037$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$6$		$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{5}+(\beta _{5}+\beta _{12})q^{7}+\beta _{13}q^{11}+\cdots$
756.2.j.a	$756$	$2$	756.j	9.c	$3$	$6$	$3$	$6.037$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$-3$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}+\beta _{3})q^{5}-\beta _{3}q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots$
756.2.j.b	$756$	$2$	756.j	9.c	$3$	$6$	$3$	$6.037$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{5}+(1-\beta _{4})q^{7}+(1-2\beta _{2}+\cdots)q^{11}+\cdots$
756.2.k.a	$756$	$2$	756.k	7.c	$3$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-3+2\zeta_{6})q^{7}-7q^{13}-8\zeta_{6}q^{19}+\cdots$
756.2.k.b	$756$	$2$	756.k	7.c	$3$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-1-2\zeta_{6})q^{7}+5q^{13}-8\zeta_{6}q^{19}+\cdots$
756.2.k.c	$756$	$2$	756.k	7.c	$3$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(3-\zeta_{6})q^{7}+2q^{13}+\zeta_{6}q^{19}+(5+\cdots)q^{25}+\cdots$
756.2.k.d	$756$	$2$	756.k	7.c	$3$	$4$	$2$	$6.037$	$\Q(\sqrt{-3}, \sqrt{10})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}+(2+3\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots$
756.2.k.e	$756$	$2$	756.k	7.c	$3$	$6$	$3$	$6.037$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
756.2.k.f	$756$	$2$	756.k	7.c	$3$	$6$	$3$	$6.037$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
756.2.l.a	$756$	$2$	756.l	63.g	$3$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{5}+(3-2\zeta_{6})q^{7}-4q^{11}+(-3+\cdots)q^{13}+\cdots$
756.2.l.b	$756$	$2$	756.l	63.g	$3$	$14$	$7$	$6.037$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-3$		$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}-\beta _{7})q^{5}-\beta _{5}q^{7}+(\beta _{9}-\beta _{13})q^{11}+\cdots$
756.2.n.a	$756$	$2$	756.n	252.n	$6$	$4$	$2$	$6.037$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots$
756.2.n.b	$756$	$2$	756.n	252.n	$6$	$84$	$42$	$6.037$		$_{}$	None	None		$4$	$0$	$1$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
756.2.o.a	$756$	$2$	756.o	252.o	$6$	$88$	$44$	$6.037$		$_{}$	None	None		$4$	$0$	$3$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
756.2.t.a	$756$	$2$	756.t	21.g	$6$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-3+\zeta_{6})q^{7}+(4-8\zeta_{6})q^{13}+(10+\cdots)q^{19}+\cdots$
756.2.t.b	$756$	$2$	756.t	21.g	$6$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1+2\zeta_{6})q^{7}+(-3+6\zeta_{6})q^{13}+(-4+\cdots)q^{19}+\cdots$
756.2.t.c	$756$	$2$	756.t	21.g	$6$	$2$	$1$	$6.037$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(3-2\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+(4-2\zeta_{6})q^{19}+\cdots$
756.2.t.d	$756$	$2$	756.t	21.g	$6$	$4$	$2$	$6.037$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-10$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+(2+4\beta _{2}+\cdots)q^{13}+\cdots$
756.2.t.e	$756$	$2$	756.t	21.g	$6$	$12$	$6$	$6.037$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{5}+\beta _{10}q^{7}+(-\beta _{3}-\beta _{5})q^{11}+\cdots$
756.2.w.a	$756$	$2$	756.w	63.i	$6$	$16$	$8$	$6.037$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-1$		$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{9}q^{5}+(\beta _{4}-\beta _{10})q^{7}-\beta _{15}q^{11}+\cdots$
756.2.x.a	$756$	$2$	756.x	63.o	$6$	$16$	$8$	$6.037$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-1$		$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{15})q^{5}+(-\beta _{6}+\beta _{13})q^{7}+\cdots$
756.2.ba.a	$756$	$2$	756.ba	36.h	$6$	$72$	$36$	$6.037$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.