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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 (22 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	7	41	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4592.2.a.a	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$2$	$0$	$-3$	$-1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-q^{7}+6q^{9}-4q^{11}+\cdots$
4592.2.a.c	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$2$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
4592.2.a.e	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$-3$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+q^{7}-2q^{9}-6q^{11}+\cdots$
4592.2.a.f	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$2$	$0$	$0$	$-4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}-3q^{9}+2q^{11}-6q^{13}+\cdots$
4592.2.a.g	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}+2q^{13}+2q^{17}+\cdots$
4592.2.a.h	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}+6q^{11}-4q^{13}+\cdots$
4592.2.a.k	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots$
4592.2.a.l	$4592$	$2$	4592.a	1.a	$1$	$1$	$1$	$36.667$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$-1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}-q^{7}+6q^{9}+2q^{11}+\cdots$
4592.2.a.o	$4592$	$2$	4592.a	1.a	$1$	$2$	$2$	$36.667$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$0$	$3$	$-3$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots$
4592.2.a.q	$4592$	$2$	4592.a	1.a	$1$	$2$	$2$	$36.667$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$3$	$-1$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots$
4592.2.a.r	$4592$	$2$	4592.a	1.a	$1$	$3$	$3$	$36.667$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$-5$	$2$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{3}+(2-2\beta _{1}+2\beta _{2})q^{5}+\cdots$
4592.2.a.t	$4592$	$2$	4592.a	1.a	$1$	$3$	$3$	$36.667$	3.3.257.1	None	✓	$1$	$0$	$0$	$1$	$6$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{3}+2q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots$
4592.2.a.v	$4592$	$2$	4592.a	1.a	$1$	$3$	$3$	$36.667$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$3$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}-q^{7}+\cdots$
4592.2.a.w	$4592$	$2$	4592.a	1.a	$1$	$3$	$3$	$36.667$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$3$	$0$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+2\beta _{2}q^{5}+q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots$
4592.2.a.x	$4592$	$2$	4592.a	1.a	$1$	$4$	$4$	$36.667$	4.4.6809.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
4592.2.a.y	$4592$	$2$	4592.a	1.a	$1$	$4$	$4$	$36.667$	4.4.107637.1	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
4592.2.a.ba	$4592$	$2$	4592.a	1.a	$1$	$4$	$4$	$36.667$	4.4.11348.1	None	✓	$1$	$0$	$0$	$1$	$3$	$4$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots$
4592.2.a.bb	$4592$	$2$	4592.a	1.a	$1$	$5$	$5$	$36.667$	5.5.633117.1	None	✓	$1$	$0$	$0$	$-4$	$-5$	$-5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots$
4592.2.a.be	$4592$	$2$	4592.a	1.a	$1$	$5$	$5$	$36.667$	5.5.470117.1	None	✓	$1$	$0$	$0$	$2$	$-1$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots$
4592.2.a.bg	$4592$	$2$	4592.a	1.a	$1$	$6$	$6$	$36.667$	6.6.185257757.1	None	✓	$1$	$0$	$0$	$4$	$-1$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{3}+(\beta _{3}-\beta _{4})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots$
4592.2.a.bh	$4592$	$2$	4592.a	1.a	$1$	$7$	$7$	$36.667$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$5$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots$
4592.2.a.bj	$4592$	$2$	4592.a	1.a	$1$	$8$	$8$	$36.667$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$-3$	$10$	$-8$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{3}+(1+\beta _{1})q^{5}-q^{7}+(2+\beta _{7})q^{9}+\cdots$

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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.