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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	5	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4235.2.a.b	$4235$	$2$	4235.a	1.a	$1$	$1$	$1$	$33.817$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots$
4235.2.a.d	$4235$	$2$	4235.a	1.a	$1$	$1$	$1$	$33.817$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$-1$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-q^{7}+\cdots$
4235.2.a.e	$4235$	$2$	4235.a	1.a	$1$	$1$	$1$	$33.817$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$1$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}-q^{7}+\cdots$
4235.2.a.h	$4235$	$2$	4235.a	1.a	$1$	$2$	$2$	$33.817$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots$
4235.2.a.i	$4235$	$2$	4235.a	1.a	$1$	$2$	$2$	$33.817$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$1$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta )q^{3}-q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
4235.2.a.j	$4235$	$2$	4235.a	1.a	$1$	$2$	$2$	$33.817$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(-1+\beta )q^{3}+3q^{4}+\cdots$
4235.2.a.k	$4235$	$2$	4235.a	1.a	$1$	$2$	$2$	$33.817$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-1$	$-2$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}-\beta q^{3}+3q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots$
4235.2.a.n	$4235$	$2$	4235.a	1.a	$1$	$2$	$2$	$33.817$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$1$	$2$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}-q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots$
4235.2.a.o	$4235$	$2$	4235.a	1.a	$1$	$3$	$3$	$33.817$	3.3.148.1	None	✓	$1$	$1$	$-1$	$0$	$3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
4235.2.a.q	$4235$	$2$	4235.a	1.a	$1$	$3$	$3$	$33.817$	3.3.148.1	None	✓	$1$	$1$	$3$	$-2$	$-3$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
4235.2.a.s	$4235$	$2$	4235.a	1.a	$1$	$4$	$4$	$33.817$	4.4.6224.1	None	✓	$1$	$1$	$-2$	$4$	$-4$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
4235.2.a.t	$4235$	$2$	4235.a	1.a	$1$	$4$	$4$	$33.817$	4.4.725.1	None	✓	$1$	$1$	$-1$	$-3$	$4$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots$
4235.2.a.u	$4235$	$2$	4235.a	1.a	$1$	$4$	$4$	$33.817$	4.4.15952.1	None	✓	$1$	$1$	$0$	$-2$	$4$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
4235.2.a.w	$4235$	$2$	4235.a	1.a	$1$	$4$	$4$	$33.817$	4.4.725.1	None	✓	$1$	$1$	$1$	$-3$	$4$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots$
4235.2.a.y	$4235$	$2$	4235.a	1.a	$1$	$5$	$5$	$33.817$	5.5.173513.1	None	✓	$1$	$1$	$-2$	$-2$	$-5$	$5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots$
4235.2.a.z	$4235$	$2$	4235.a	1.a	$1$	$5$	$5$	$33.817$	5.5.270017.1	None	✓	$1$	$1$	$-2$	$2$	$5$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{4})q^{4}+q^{5}+\cdots$
4235.2.a.bb	$4235$	$2$	4235.a	1.a	$1$	$5$	$5$	$33.817$	5.5.580017.1	None	✓	$1$	$1$	$0$	$-2$	$-5$	$5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{3}-\beta _{4})q^{4}-q^{5}+\cdots$
4235.2.a.bc	$4235$	$2$	4235.a	1.a	$1$	$5$	$5$	$33.817$	5.5.288385.1	None	✓	$1$	$1$	$0$	$2$	$5$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
4235.2.a.bg	$4235$	$2$	4235.a	1.a	$1$	$8$	$8$	$33.817$	8.8.$\cdots$.1	None	✓	$1$	$1$	$-2$	$-3$	$-8$	$-8$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$
4235.2.a.bh	$4235$	$2$	4235.a	1.a	$1$	$8$	$8$	$33.817$	8.8.$\cdots$.1	None	✓	$1$	$1$	$2$	$-3$	$-8$	$8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$
4235.2.a.bi	$4235$	$2$	4235.a	1.a	$1$	$10$	$10$	$33.817$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-2$	$-4$	$10$	$10$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
4235.2.a.bj	$4235$	$2$	4235.a	1.a	$1$	$10$	$10$	$33.817$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-2$	$4$	$-10$	$-10$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$

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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.