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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 (1-50 of 144 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
925.2.a.a	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}-2q^{6}+2q^{7}+3q^{8}+\cdots$
925.2.a.b	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{7}-2q^{9}+3q^{11}+\cdots$
925.2.a.c	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{7}-2q^{9}-5q^{11}+\cdots$
925.2.a.d	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+5q^{7}+\cdots$
925.2.a.e	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	$\Q$	None	✓	$1$	$0$	$2$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}+6q^{6}+q^{7}+\cdots$
925.2.a.f	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.973904.1	None	✓	$1$	$1$	$-2$	$-3$	$0$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{3})q^{4}+\cdots$
925.2.a.g	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.65657.1	None	✓	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots$
925.2.a.h	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.368464.1	None	✓	$1$	$0$	$0$	$1$	$0$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}+(2-\beta _{1}-\beta _{4})q^{4}+\cdots$
925.2.a.i	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.65657.1	None	✓	$1$	$1$	$1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots$
925.2.a.j	$925$	$2$	925.a	1.a	$1$	$7$	$7$	$7.386$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-1$	$1$	$0$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots$
925.2.a.k	$925$	$2$	925.a	1.a	$1$	$7$	$7$	$7.386$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots$
925.2.a.l	$925$	$2$	925.a	1.a	$1$	$9$	$9$	$7.386$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-5$	$-8$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{6})q^{3}+(2+\cdots)q^{4}+\cdots$
925.2.a.m	$925$	$2$	925.a	1.a	$1$	$9$	$9$	$7.386$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$5$	$8$	$0$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{6})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
925.2.b.a	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+5iq^{7}+\cdots$
925.2.b.b	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-3iq^{3}-2q^{4}+6q^{6}+iq^{7}+\cdots$
925.2.b.c	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-2iq^{7}+\cdots$
925.2.b.d	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+2q^{4}+3iq^{7}+2q^{9}-5q^{11}+\cdots$
925.2.b.e	$925$	$2$	925.b	5.b	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+2q^{4}-iq^{7}+2q^{9}+3q^{11}+\cdots$
925.2.b.f	$925$	$2$	925.b	5.b	$2$	$10$	$10$	$7.386$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{8})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots$
925.2.b.g	$925$	$2$	925.b	5.b	$2$	$10$	$10$	$7.386$	10.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-\beta _{7}q^{3}+(-2+\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots$
925.2.b.h	$925$	$2$	925.b	5.b	$2$	$10$	$10$	$7.386$	10.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots$
925.2.b.i	$925$	$2$	925.b	5.b	$2$	$14$	$14$	$7.386$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$
925.2.c.a	$925$	$2$	925.c	37.b	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-2$	$0$	$-2$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2q^{4}-q^{7}-2q^{9}-3q^{11}+\cdots$
925.2.c.b	$925$	$2$	925.c	37.b	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$2$	$0$	$-6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-2q^{4}+iq^{6}-3q^{7}+\cdots$
925.2.c.c	$925$	$2$	925.c	37.b	$2$	$12$	$12$	$7.386$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$18$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1+\beta _{9}+\beta _{10}+\cdots)q^{4}+\cdots$
925.2.c.d	$925$	$2$	925.c	37.b	$2$	$12$	$12$	$7.386$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$0$		$7$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{2})q^{4}-\beta _{6}q^{6}+\cdots$
925.2.c.e	$925$	$2$	925.c	37.b	$2$	$12$	$12$	$7.386$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$2$	$0$	$0$		$7$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{2})q^{4}+\beta _{6}q^{6}+\cdots$
925.2.c.f	$925$	$2$	925.c	37.b	$2$	$16$	$16$	$7.386$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+\beta _{9}q^{3}+(-1-\beta _{2})q^{4}+\beta _{13}q^{6}+\cdots$
925.2.d.a	$925$	$2$	925.d	185.d	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{2}-iq^{3}+2q^{4}+2iq^{6}-3iq^{7}+\cdots$
925.2.d.b	$925$	$2$	925.d	185.d	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}-2q^{4}+iq^{7}+2q^{9}-3q^{11}+\cdots$
925.2.d.c	$925$	$2$	925.d	185.d	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}-2q^{4}+iq^{7}+2q^{9}-3q^{11}+\cdots$
925.2.d.d	$925$	$2$	925.d	185.d	$2$	$2$	$2$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}-iq^{3}+2q^{4}-2iq^{6}-3iq^{7}+\cdots$
925.2.d.e	$925$	$2$	925.d	185.d	$2$	$12$	$12$	$7.386$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{2}q^{3}+(2-\beta _{1})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
925.2.d.f	$925$	$2$	925.d	185.d	$2$	$12$	$12$	$7.386$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$2$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(2-\beta _{1})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
925.2.d.g	$925$	$2$	925.d	185.d	$2$	$24$	$24$	$7.386$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
925.2.e.a	$925$	$2$	925.e	37.c	$3$	$2$	$1$	$7.386$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{7}+3q^{8}+\cdots$
925.2.e.b	$925$	$2$	925.e	37.c	$3$	$14$	$7$	$7.386$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$-2$	$2$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{8}q^{2}-\beta _{6}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$
925.2.e.c	$925$	$2$	925.e	37.c	$3$	$14$	$7$	$7.386$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{2}+\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots$
925.2.e.d	$925$	$2$	925.e	37.c	$3$	$24$	$12$	$7.386$		None		$2$	$0$	$-1$	$-2$	$0$	$-6$			$\mathrm{SU}(2)[C_{3}]$
925.2.e.e	$925$	$2$	925.e	37.c	$3$	$24$	$12$	$7.386$		None		$2$	$0$	$1$	$2$	$0$	$6$			$\mathrm{SU}(2)[C_{3}]$
925.2.e.f	$925$	$2$	925.e	37.c	$3$	$36$	$18$	$7.386$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
925.2.f.a	$925$	$2$	925.f	185.f	$4$	$2$	$1$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+(-2-2i)q^{3}+q^{4}+(2-2i)q^{6}+\cdots$
925.2.f.b	$925$	$2$	925.f	185.f	$4$	$2$	$1$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+(1+i)q^{3}+q^{4}+(-1+i)q^{6}+\cdots$
925.2.f.c	$925$	$2$	925.f	185.f	$4$	$6$	$3$	$7.386$	6.0.350464.1	None		$2$	$0$	$0$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots$
925.2.f.d	$925$	$2$	925.f	185.f	$4$	$24$	$12$	$7.386$		None		$2$	$0$	$0$	$-4$	$0$	$-6$			$\mathrm{SU}(2)[C_{4}]$
925.2.f.e	$925$	$2$	925.f	185.f	$4$	$28$	$14$	$7.386$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
925.2.f.f	$925$	$2$	925.f	185.f	$4$	$48$	$24$	$7.386$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
925.2.k.a	$925$	$2$	925.k	185.k	$4$	$2$	$1$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$-2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-1+i)q^{3}-q^{4}+(-1+i)q^{6}+\cdots$
925.2.k.b	$925$	$2$	925.k	185.k	$4$	$2$	$1$	$7.386$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(2-2i)q^{3}-q^{4}+(2-2i)q^{6}+\cdots$
925.2.k.c	$925$	$2$	925.k	185.k	$4$	$6$	$3$	$7.386$	6.0.350464.1	None		$2$	$0$	$2$	$-2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.