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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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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 (26 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	5	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5915.2.a.a	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-q^{7}-3q^{9}-2q^{10}+\cdots$
5915.2.a.b	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$-2$	$1$	$1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-q^{7}+\cdots$
5915.2.a.c	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$-2$	$3$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+2q^{4}-q^{5}-6q^{6}+\cdots$
5915.2.a.e	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
5915.2.a.f	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots$
5915.2.a.g	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots$
5915.2.a.h	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
5915.2.a.i	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots$
5915.2.a.j	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots$
5915.2.a.k	$5915$	$2$	5915.a	1.a	$1$	$1$	$1$	$47.232$	$\Q$	None	✓	$1$	$0$	$2$	$3$	$1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots$
5915.2.a.l	$5915$	$2$	5915.a	1.a	$1$	$2$	$2$	$47.232$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$1$	$-1$	$-2$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}-q^{5}+\cdots$
5915.2.a.m	$5915$	$2$	5915.a	1.a	$1$	$4$	$4$	$47.232$	4.4.1957.1	None	✓	$1$	$0$	$-3$	$4$	$-4$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+\cdots$
5915.2.a.v	$5915$	$2$	5915.a	1.a	$1$	$6$	$6$	$47.232$	6.6.3728753.1	None	✓	$1$	$0$	$-2$	$-1$	$6$	$-6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{4}-\beta _{5})q^{3}+\cdots$
5915.2.a.x	$5915$	$2$	5915.a	1.a	$1$	$7$	$7$	$47.232$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-1$	$0$	$-7$	$7$	$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots$
5915.2.a.y	$5915$	$2$	5915.a	1.a	$1$	$7$	$7$	$47.232$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-1$	$-7$	$7$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
5915.2.a.z	$5915$	$2$	5915.a	1.a	$1$	$7$	$7$	$47.232$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-1$	$7$	$-7$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
5915.2.a.ba	$5915$	$2$	5915.a	1.a	$1$	$7$	$7$	$47.232$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$7$	$-7$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(2+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
5915.2.a.bb	$5915$	$2$	5915.a	1.a	$1$	$7$	$7$	$47.232$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$1$	$0$	$7$	$-7$	$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots$
5915.2.a.bc	$5915$	$2$	5915.a	1.a	$1$	$9$	$9$	$47.232$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$-9$	$-9$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
5915.2.a.bd	$5915$	$2$	5915.a	1.a	$1$	$9$	$9$	$47.232$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$9$	$9$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
5915.2.a.bj	$5915$	$2$	5915.a	1.a	$1$	$15$	$15$	$47.232$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$1$	$5$	$-15$	$15$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
5915.2.a.bk	$5915$	$2$	5915.a	1.a	$1$	$15$	$15$	$47.232$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$2$	$-6$	$15$	$-15$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{14}q^{3}+(2-\beta _{10}+\beta _{11}+\cdots)q^{4}+\cdots$
5915.2.a.bl	$5915$	$2$	5915.a	1.a	$1$	$15$	$15$	$47.232$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$7$	$-7$	$-15$	$-15$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
5915.2.a.bm	$5915$	$2$	5915.a	1.a	$1$	$18$	$18$	$47.232$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$-18$	$-18$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
5915.2.a.bn	$5915$	$2$	5915.a	1.a	$1$	$18$	$18$	$47.232$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$18$	$18$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
5915.2.a.bp	$5915$	$2$	5915.a	1.a	$1$	$21$	$21$	$47.232$		None	✓	$1$	$0$	$4$	$5$	$21$	$21$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.