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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 (38 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8450.2.a.c	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
8450.2.a.d	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
8450.2.a.f	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots$
8450.2.a.g	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{7}-q^{8}-3q^{9}-3q^{11}+\cdots$
8450.2.a.i	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-4q^{7}-q^{8}+\cdots$
8450.2.a.j	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots$
8450.2.a.k	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots$
8450.2.a.o	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
8450.2.a.p	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots$
8450.2.a.u	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
8450.2.a.v	$8450$	$2$	8450.a	1.a	$1$	$1$	$1$	$67.474$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
8450.2.a.z	$8450$	$2$	8450.a	1.a	$1$	$2$	$2$	$67.474$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots$
8450.2.a.bc	$8450$	$2$	8450.a	1.a	$1$	$2$	$2$	$67.474$	$\Q(\sqrt{10}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots$
8450.2.a.bd	$8450$	$2$	8450.a	1.a	$1$	$2$	$2$	$67.474$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$1$	$0$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(-3+\beta )q^{7}+\cdots$
8450.2.a.be	$8450$	$2$	8450.a	1.a	$1$	$2$	$2$	$67.474$	$\Q(\sqrt{21}) $	None	✓	$1$	$1$	$-2$	$1$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(1-\beta )q^{7}+\cdots$
8450.2.a.bh	$8450$	$2$	8450.a	1.a	$1$	$2$	$2$	$67.474$	$\Q(\sqrt{21}) $	None	✓	$1$	$1$	$2$	$-1$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+(-1+\beta )q^{7}+\cdots$
8450.2.a.bi	$8450$	$2$	8450.a	1.a	$1$	$2$	$2$	$67.474$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$-1$	$0$	$5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+(3-\beta )q^{7}+\cdots$
8450.2.a.bm	$8450$	$2$	8450.a	1.a	$1$	$2$	$2$	$67.474$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$2$	$0$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
8450.2.a.bn	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-3$	$-3$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots$
8450.2.a.bo	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-3$	$-1$	$0$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
8450.2.a.bp	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-3$	$-1$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
8450.2.a.bq	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	3.3.2808.1	None	✓	$1$	$1$	$-3$	$0$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
8450.2.a.bw	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-3$	$1$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
8450.2.a.bx	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$-3$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{6}+\cdots$
8450.2.a.by	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$-1$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-2+\cdots)q^{7}+\cdots$
8450.2.a.bz	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$-1$	$0$	$5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
8450.2.a.ca	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	3.3.148.1	None	✓	$1$	$1$	$3$	$0$	$0$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(-2+\cdots)q^{7}+\cdots$
8450.2.a.cb	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	3.3.148.1	None	✓	$1$	$1$	$3$	$0$	$0$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}+(-2+\cdots)q^{7}+\cdots$
8450.2.a.cc	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	3.3.940.1	None	✓	$1$	$1$	$3$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
8450.2.a.cd	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	3.3.2808.1	None	✓	$1$	$1$	$3$	$0$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
8450.2.a.cf	$8450$	$2$	8450.a	1.a	$1$	$3$	$3$	$67.474$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$1$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-2+\cdots)q^{7}+\cdots$
8450.2.a.cj	$8450$	$2$	8450.a	1.a	$1$	$4$	$4$	$67.474$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓	$2$	$1$	$-4$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+\beta _{2}q^{7}+\cdots$
8450.2.a.ck	$8450$	$2$	8450.a	1.a	$1$	$4$	$4$	$67.474$	4.4.4752.1	None	✓	$1$	$1$	$-4$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
8450.2.a.cl	$8450$	$2$	8450.a	1.a	$1$	$4$	$4$	$67.474$	4.4.4752.1	None	✓	$1$	$1$	$4$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
8450.2.a.cm	$8450$	$2$	8450.a	1.a	$1$	$4$	$4$	$67.474$	4.4.4752.1	None	✓	$1$	$1$	$4$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{6}+\cdots$
8450.2.a.cr	$8450$	$2$	8450.a	1.a	$1$	$8$	$8$	$67.474$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$1$	$-8$	$0$	$0$	$-10$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
8450.2.a.ct	$8450$	$2$	8450.a	1.a	$1$	$9$	$9$	$67.474$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-9$	$-7$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{4})q^{3}+q^{4}+(1+\beta _{4}+\cdots)q^{6}+\cdots$
8450.2.a.cx	$8450$	$2$	8450.a	1.a	$1$	$9$	$9$	$67.474$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$9$	$-7$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{4})q^{3}+q^{4}+(-1-\beta _{4}+\cdots)q^{6}+\cdots$

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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.