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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 (30 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				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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	5	31	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4805.2.a.a	$4805$	$2$	4805.a	1.a	$1$	$1$	$1$	$38.368$	$\Q$	None	✓				155.2.e.a	$1$	$1$	$-2$	$-2$	$1$	$4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots$
4805.2.a.b	$4805$	$2$	4805.a	1.a	$1$	$1$	$1$	$38.368$	$\Q$	None	✓				155.2.a.a	$1$	$1$	$-2$	$1$	$1$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots$
4805.2.a.c	$4805$	$2$	4805.a	1.a	$1$	$1$	$1$	$38.368$	$\Q$	None	✓				155.2.e.a	$1$	$0$	$-2$	$2$	$1$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
4805.2.a.d	$4805$	$2$	4805.a	1.a	$1$	$1$	$1$	$38.368$	$\Q$	None	✓				155.2.a.b	$1$	$0$	$-1$	$-2$	$-1$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}+4q^{7}+\cdots$
4805.2.a.e	$4805$	$2$	4805.a	1.a	$1$	$1$	$1$	$38.368$	$\Q$	None	✓				155.2.a.c	$1$	$0$	$0$	$1$	$-1$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-2q^{9}+4q^{11}+\cdots$
4805.2.a.f	$4805$	$2$	4805.a	1.a	$1$	$1$	$1$	$38.368$	$\Q$	None	✓				155.2.e.b	$1$	$0$	$2$	$-2$	$-1$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}-q^{5}-4q^{6}+\cdots$
4805.2.a.g	$4805$	$2$	4805.a	1.a	$1$	$1$	$1$	$38.368$	$\Q$	None	✓				155.2.e.b	$1$	$1$	$2$	$2$	$-1$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
4805.2.a.h	$4805$	$2$	4805.a	1.a	$1$	$2$	$2$	$38.368$	$\Q(\sqrt{2}) $	None	✓	✓			4805.2.a.h	$2$	$0$	$-2$	$0$	$-2$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}-q^{4}-q^{5}-\beta q^{6}-2q^{7}+\cdots$
4805.2.a.i	$4805$	$2$	4805.a	1.a	$1$	$4$	$4$	$38.368$	4.4.9301.1	None	✓				155.2.e.c	$1$	$1$	$-1$	$-3$	$-4$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
4805.2.a.j	$4805$	$2$	4805.a	1.a	$1$	$4$	$4$	$38.368$	4.4.20308.1	None	✓				155.2.a.d	$1$	$0$	$-1$	$1$	$-4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots$
4805.2.a.k	$4805$	$2$	4805.a	1.a	$1$	$4$	$4$	$38.368$	4.4.9301.1	None	✓				155.2.e.c	$1$	$0$	$-1$	$3$	$-4$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
4805.2.a.l	$4805$	$2$	4805.a	1.a	$1$	$4$	$4$	$38.368$	4.4.31744.1	None	✓	✓			4805.2.a.l	$2$	$1$	$0$	$0$	$4$	$-8$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{3})q^{6}+\cdots$
4805.2.a.m	$4805$	$2$	4805.a	1.a	$1$	$4$	$4$	$38.368$	4.4.725.1	None	✓				155.2.e.d	$1$	$1$	$1$	$-1$	$4$	$-1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{1}+2\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
4805.2.a.n	$4805$	$2$	4805.a	1.a	$1$	$4$	$4$	$38.368$	4.4.8468.1	None	✓				155.2.a.e	$1$	$1$	$1$	$-1$	$4$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots$
4805.2.a.o	$4805$	$2$	4805.a	1.a	$1$	$4$	$4$	$38.368$	4.4.725.1	None	✓				155.2.e.d	$1$	$0$	$1$	$1$	$4$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}-2\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
4805.2.a.p	$4805$	$2$	4805.a	1.a	$1$	$6$	$6$	$38.368$	6.6.12781568.1	None	✓	✓			4805.2.a.p	$2$	$0$	$2$	$0$	$-6$	$4$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{5})q^{4}-q^{5}+\cdots$
4805.2.a.q	$4805$	$2$	4805.a	1.a	$1$	$8$	$8$	$38.368$	8.8.$\cdots$.1	None	✓	✓			4805.2.a.q	$2$	$1$	$-4$	$0$	$8$	$-8$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{2}-\beta _{4})q^{4}+\cdots$
4805.2.a.r	$4805$	$2$	4805.a	1.a	$1$	$10$	$10$	$38.368$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓			4805.2.a.r	$2$	$0$	$2$	$0$	$-10$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(\beta _{3}-\beta _{6})q^{3}+(2+\beta _{7})q^{4}+\cdots$
4805.2.a.s	$4805$	$2$	4805.a	1.a	$1$	$12$	$12$	$38.368$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				155.2.h.a	$1$	$1$	$-1$	$-8$	$12$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
4805.2.a.t	$4805$	$2$	4805.a	1.a	$1$	$12$	$12$	$38.368$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				155.2.h.a	$1$	$0$	$-1$	$8$	$12$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
4805.2.a.u	$4805$	$2$	4805.a	1.a	$1$	$12$	$12$	$38.368$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				155.2.h.b	$1$	$1$	$1$	$0$	$-12$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+\cdots$
4805.2.a.v	$4805$	$2$	4805.a	1.a	$1$	$12$	$12$	$38.368$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				155.2.h.b	$1$	$0$	$1$	$0$	$-12$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+\cdots$
4805.2.a.w	$4805$	$2$	4805.a	1.a	$1$	$16$	$16$	$38.368$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓			4805.2.a.w	$2$	$1$	$-8$	$0$	$16$	$-24$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{8}q^{2}+\beta _{1}q^{3}+(1+\beta _{3}-\beta _{7}+\beta _{8}+\cdots)q^{4}+\cdots$
4805.2.a.x	$4805$	$2$	4805.a	1.a	$1$	$20$	$20$	$38.368$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓				155.2.q.a	$1$	$1$	$-1$	$-4$	$-20$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{19}q^{3}+(1+\beta _{9}+\beta _{10}+\cdots)q^{4}+\cdots$
4805.2.a.y	$4805$	$2$	4805.a	1.a	$1$	$20$	$20$	$38.368$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓				155.2.q.a	$1$	$0$	$-1$	$4$	$-20$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{19}q^{3}+(1+\beta _{9}+\beta _{10}+\cdots)q^{4}+\cdots$
4805.2.a.z	$4805$	$2$	4805.a	1.a	$1$	$20$	$20$	$38.368$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓		✓		155.2.q.b	$1$	$1$	$1$	$-12$	$20$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{13})q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots$
4805.2.a.ba	$4805$	$2$	4805.a	1.a	$1$	$20$	$20$	$38.368$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓				155.2.q.b	$1$	$0$	$1$	$12$	$20$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{13})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
4805.2.a.bb	$4805$	$2$	4805.a	1.a	$1$	$24$	$24$	$38.368$		None	✓	✓	✓		4805.2.a.bb	$2$	$0$	$0$	$0$	$-24$	$8$	$+$	$-$	$-$		$\mathrm{SU}(2)$
4805.2.a.bc	$4805$	$2$	4805.a	1.a	$1$	$32$	$32$	$38.368$		None	✓	✓	✓		4805.2.a.bc	$2$	$1$	$0$	$0$	$-32$	$-16$	$+$	$+$	$+$		$\mathrm{SU}(2)$
4805.2.a.bd	$4805$	$2$	4805.a	1.a	$1$	$48$	$48$	$38.368$		None	✓	✓	✓		4805.2.a.bd	$2$	$0$	$16$	$0$	$48$	$48$	$-$	$+$	$-$		$\mathrm{SU}(2)$

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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.