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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (27 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4248.2.a.a	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓	✓			4248.2.a.a	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+4q^{7}+4q^{11}+2q^{13}-4q^{17}+\cdots$
4248.2.a.b	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓	✓			4248.2.a.b	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{11}-4q^{19}-q^{25}-6q^{29}+\cdots$
4248.2.a.c	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓				472.2.a.d	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-q^{11}-q^{13}+q^{17}+\cdots$
4248.2.a.d	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓				472.2.a.c	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots$
4248.2.a.e	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓				472.2.a.b	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-2q^{13}+6q^{17}+3q^{19}+\cdots$
4248.2.a.f	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓				472.2.a.a	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}+4q^{11}+6q^{13}+6q^{17}+\cdots$
4248.2.a.g	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓	✓			4248.2.a.b	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{11}-4q^{19}-q^{25}+6q^{29}+\cdots$
4248.2.a.h	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓				472.2.a.e	$1$	$1$	$0$	$0$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+3q^{7}-6q^{11}-6q^{13}+2q^{17}+\cdots$
4248.2.a.i	$4248$	$2$	4248.a	1.a	$1$	$1$	$1$	$33.920$	$\Q$	None	✓	✓			4248.2.a.a	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+4q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots$
4248.2.a.j	$4248$	$2$	4248.a	1.a	$1$	$2$	$2$	$33.920$	$\Q(\sqrt{5}) $	None	✓				1416.2.a.b	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1-\beta )q^{7}+q^{11}-3q^{13}+\cdots$
4248.2.a.k	$4248$	$2$	4248.a	1.a	$1$	$2$	$2$	$33.920$	$\Q(\sqrt{5}) $	None	✓				1416.2.a.a	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-2+\beta )q^{7}+(1+2\beta )q^{11}+\cdots$
4248.2.a.l	$4248$	$2$	4248.a	1.a	$1$	$3$	$3$	$33.920$	3.3.229.1	None	✓				1416.2.a.e	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots$
4248.2.a.m	$4248$	$2$	4248.a	1.a	$1$	$3$	$3$	$33.920$	3.3.621.1	None	✓				1416.2.a.d	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+3q^{11}+\cdots$
4248.2.a.n	$4248$	$2$	4248.a	1.a	$1$	$3$	$3$	$33.920$	3.3.229.1	None	✓				1416.2.a.c	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+(-1-2\beta _{1}+\cdots)q^{11}+\cdots$
4248.2.a.o	$4248$	$2$	4248.a	1.a	$1$	$4$	$4$	$33.920$	4.4.27004.1	None	✓		✓		1416.2.a.f	$1$	$1$	$0$	$0$	$-4$	$1$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+\beta _{1}q^{7}+(1-\beta _{3})q^{11}+\cdots$
4248.2.a.p	$4248$	$2$	4248.a	1.a	$1$	$4$	$4$	$33.920$	4.4.6809.1	None	✓				472.2.a.f	$1$	$0$	$0$	$0$	$3$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{3})q^{5}+(-2-2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
4248.2.a.q	$4248$	$2$	4248.a	1.a	$1$	$5$	$5$	$33.920$	5.5.1815152.1	None	✓	✓	✓		4248.2.a.q	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{3}q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots$
4248.2.a.r	$4248$	$2$	4248.a	1.a	$1$	$5$	$5$	$33.920$	5.5.5755900.1	None	✓		✓		1416.2.a.g	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+(-\beta _{3}+\beta _{4})q^{11}+\cdots$
4248.2.a.s	$4248$	$2$	4248.a	1.a	$1$	$5$	$5$	$33.920$	5.5.1815152.1	None	✓	✓	✓		4248.2.a.q	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{3}q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots$
4248.2.a.t	$4248$	$2$	4248.a	1.a	$1$	$6$	$6$	$33.920$	6.6.921465377.1	None	✓		✓		472.2.a.g	$1$	$1$	$0$	$0$	$-7$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(-1-\beta _{4})q^{7}+\beta _{3}q^{11}+\cdots$
4248.2.a.u	$4248$	$2$	4248.a	1.a	$1$	$6$	$6$	$33.920$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓		✓		1416.2.a.h	$1$	$0$	$0$	$0$	$-6$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(1-\beta _{3})q^{7}+\beta _{5}q^{11}+\cdots$
4248.2.a.v	$4248$	$2$	4248.a	1.a	$1$	$8$	$8$	$33.920$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		4248.2.a.v	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+\beta _{6}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
4248.2.a.w	$4248$	$2$	4248.a	1.a	$1$	$8$	$8$	$33.920$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		4248.2.a.v	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+\beta _{6}q^{7}+(1-\beta _{1}+\beta _{4}+\cdots)q^{11}+\cdots$
4248.2.h.a	$4248$	$2$	4248.h	177.d	$2$	$2$	$2$	$33.920$	$\Q(\sqrt{-2}) $	None		✓			4248.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-6q^{11}+2\beta q^{13}+\beta q^{17}+\cdots$
4248.2.h.b	$4248$	$2$	4248.h	177.d	$2$	$2$	$2$	$33.920$	$\Q(\sqrt{-2}) $	None		✓			4248.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+6q^{11}-2\beta q^{13}+\beta q^{17}+\cdots$
4248.2.h.c	$4248$	$2$	4248.h	177.d	$2$	$28$	$28$	$33.920$		None		✓			4248.2.h.c	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
4248.2.h.d	$4248$	$2$	4248.h	177.d	$2$	$28$	$28$	$33.920$		None		✓			4248.2.h.c	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.