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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 380 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
75.2.a.a	$75$	$2$	75.a	1.a	$1$	$1$	$1$	$0.599$	$\Q$	None	✓	$1$	$0$	$-2$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}+3q^{7}+\cdots$
75.2.a.b	$75$	$2$	75.a	1.a	$1$	$1$	$1$	$0.599$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
75.2.a.c	$75$	$2$	75.a	1.a	$1$	$1$	$1$	$0.599$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots$
75.2.b.a	$75$	$2$	75.b	5.b	$2$	$2$	$2$	$0.599$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}-3iq^{7}+\cdots$
75.2.b.b	$75$	$2$	75.b	5.b	$2$	$2$	$2$	$0.599$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots$
75.2.e.a	$75$	$2$	75.e	15.e	$4$	$4$	$2$	$0.599$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-15}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-3q^{6}-\beta _{3}q^{8}+\cdots$
75.2.e.b	$75$	$2$	75.e	15.e	$4$	$4$	$2$	$0.599$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-3}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}-2\beta _{2}q^{4}+\beta _{3}q^{7}+3\beta _{2}q^{9}+\cdots$
75.2.g.a	$75$	$2$	75.g	25.d	$5$	$4$	$1$	$0.599$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$-1$	$5$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
75.2.g.b	$75$	$2$	75.g	25.d	$5$	$8$	$2$	$0.599$	8.0.26265625.1	None		$2$	$0$	$-1$	$-2$	$-5$	$4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}-\beta _{7})q^{2}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$
75.2.g.c	$75$	$2$	75.g	25.d	$5$	$12$	$3$	$0.599$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$3$	$-6$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots$
75.2.i.a	$75$	$2$	75.i	25.e	$10$	$16$	$4$	$0.599$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\beta _{2}-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{2}+\cdots$
75.2.l.a	$75$	$2$	75.l	75.l	$20$	$64$	$8$	$0.599$		None		$4$	$0$	$0$	$-10$	$0$	$-20$			$\mathrm{SU}(2)[C_{20}]$
75.3.c.a	$75$	$3$	75.c	3.b	$2$	$1$	$1$	$2.044$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-3$	$0$	$11$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}+11q^{7}+9q^{9}-12q^{12}+\cdots$
75.3.c.b	$75$	$3$	75.c	3.b	$2$	$1$	$1$	$2.044$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$3$	$0$	$-11$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+4q^{4}-11q^{7}+9q^{9}+12q^{12}+\cdots$
75.3.c.c	$75$	$3$	75.c	3.b	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-11}) $	None		$2$	$0$	$0$	$-5$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\beta )q^{2}+(-2-\beta )q^{3}-7q^{4}+\cdots$
75.3.c.d	$75$	$3$	75.c	3.b	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-15}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}+3iq^{3}+3q^{4}-3q^{6}+7iq^{8}+\cdots$
75.3.c.e	$75$	$3$	75.c	3.b	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(2-\beta )q^{3}-q^{4}+(5+2\beta )q^{6}+\cdots$
75.3.c.f	$75$	$3$	75.c	3.b	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-11}) $	None		$2$	$0$	$0$	$5$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\beta )q^{2}+(3-\beta )q^{3}-7q^{4}+(-3+\cdots)q^{6}+\cdots$
75.3.d.a	$75$	$3$	75.d	15.d	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3iq^{3}-4q^{4}+11iq^{7}-9q^{9}-12iq^{12}+\cdots$
75.3.d.b	$75$	$3$	75.d	15.d	$2$	$4$	$4$	$2.044$	$\Q(i, \sqrt{5})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(5-\beta _{2}+\cdots)q^{6}+\cdots$
75.3.d.c	$75$	$3$	75.d	15.d	$2$	$4$	$4$	$2.044$	$\Q(i, \sqrt{11})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+7q^{4}+(-6+\cdots)q^{6}+\cdots$
75.3.f.a	$75$	$3$	75.f	5.c	$4$	$4$	$2$	$2.044$	$\Q(i, \sqrt{6})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+3q^{6}+6\beta _{1}q^{7}+\cdots$
75.3.f.b	$75$	$3$	75.f	5.c	$4$	$4$	$2$	$2.044$	$\Q(i, \sqrt{6})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2\beta _{1}q^{2}-\beta _{3}q^{3}+8\beta _{2}q^{4}+6q^{6}+\cdots$
75.3.f.c	$75$	$3$	75.f	5.c	$4$	$4$	$2$	$2.044$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$4$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
75.3.h.a	$75$	$3$	75.h	75.h	$10$	$72$	$18$	$2.044$		None		$4$	$0$	$0$	$-5$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
75.3.j.a	$75$	$3$	75.j	75.j	$10$	$72$	$18$	$2.044$		None		$4$	$0$	$0$	$-1$	$0$	$-8$			$\mathrm{SU}(2)[C_{10}]$
75.3.k.a	$75$	$3$	75.k	25.f	$20$	$80$	$10$	$2.044$		None		$2$	$0$	$4$	$0$	$4$	$-4$			$\mathrm{SU}(2)[C_{20}]$
75.4.a.a	$75$	$4$	75.a	1.a	$1$	$1$	$1$	$4.425$	$\Q$	None	✓	$1$	$1$	$-3$	$3$	$0$	$-20$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+3q^{3}+q^{4}-9q^{6}-20q^{7}+\cdots$
75.4.a.b	$75$	$4$	75.a	1.a	$1$	$1$	$1$	$4.425$	$\Q$	None	✓	$1$	$0$	$-1$	$-3$	$0$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-7q^{4}+3q^{6}+24q^{7}+\cdots$
75.4.a.c	$75$	$4$	75.a	1.a	$1$	$2$	$2$	$4.425$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$-3$	$-6$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-3q^{3}+(3+3\beta )q^{4}+\cdots$
75.4.a.d	$75$	$4$	75.a	1.a	$1$	$2$	$2$	$4.425$	$\Q(\sqrt{19}) $	None	✓	$1$	$0$	$-2$	$6$	$0$	$26$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+3q^{3}+(12-2\beta )q^{4}+\cdots$
75.4.a.e	$75$	$4$	75.a	1.a	$1$	$2$	$2$	$4.425$	$\Q(\sqrt{19}) $	None	✓	$1$	$0$	$2$	$-6$	$0$	$-26$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-3q^{3}+(12+2\beta )q^{4}+(-3+\cdots)q^{6}+\cdots$
75.4.a.f	$75$	$4$	75.a	1.a	$1$	$2$	$2$	$4.425$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$3$	$6$	$0$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}+(3+\cdots)q^{6}+\cdots$
75.4.b.a	$75$	$4$	75.b	5.b	$2$	$2$	$2$	$4.425$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{2}+3iq^{3}-q^{4}-9q^{6}+20iq^{7}+\cdots$
75.4.b.b	$75$	$4$	75.b	5.b	$2$	$2$	$2$	$4.425$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}-24iq^{7}+\cdots$
75.4.b.c	$75$	$4$	75.b	5.b	$2$	$4$	$4$	$4.425$	$\Q(i, \sqrt{19})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(-12+\cdots)q^{4}+\cdots$
75.4.e.a	$75$	$4$	75.e	15.e	$4$	$4$	$2$	$4.425$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-3}) $		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}-8\beta _{2}q^{4}-6\beta _{3}q^{7}+3^{3}\beta _{2}q^{9}+\cdots$
75.4.e.b	$75$	$4$	75.e	15.e	$4$	$4$	$2$	$4.425$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-15}) $		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+19\beta _{2}q^{4}+3^{3}q^{6}+\cdots$
75.4.e.c	$75$	$4$	75.e	15.e	$4$	$8$	$4$	$4.425$	8.0.$\cdots$.8	None		$4$	$0$	$0$	$6$	$0$	$16$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6}-\beta _{7})q^{3}+\cdots$
75.4.e.d	$75$	$4$	75.e	15.e	$4$	$16$	$8$	$4.425$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{8}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}-\beta _{8}q^{3}+(6\beta _{1}+\beta _{5})q^{4}+(-6+\cdots)q^{6}+\cdots$
75.4.g.a	$75$	$4$	75.g	25.d	$5$	$28$	$7$	$4.425$		None		$2$	$0$	$-4$	$21$	$15$	$58$			$\mathrm{SU}(2)[C_{5}]$
75.4.g.b	$75$	$4$	75.g	25.d	$5$	$28$	$7$	$4.425$		None		$2$	$0$	$0$	$-21$	$-15$	$-54$			$\mathrm{SU}(2)[C_{5}]$
75.4.i.a	$75$	$4$	75.i	25.e	$10$	$64$	$16$	$4.425$		None		$2$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{10}]$
75.4.l.a	$75$	$4$	75.l	75.l	$20$	$224$	$28$	$4.425$		None		$4$	$0$	$0$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{20}]$
75.5.c.a	$75$	$5$	75.c	3.b	$2$	$1$	$1$	$7.753$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-9$	$0$	$-23$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-9q^{3}+2^{4}q^{4}-23q^{7}+3^{4}q^{9}-12^{2}q^{12}+\cdots$
75.5.c.b	$75$	$5$	75.c	3.b	$2$	$1$	$1$	$7.753$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$9$	$0$	$23$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}+2^{4}q^{4}+23q^{7}+3^{4}q^{9}+12^{2}q^{12}+\cdots$
75.5.c.c	$75$	$5$	75.c	3.b	$2$	$2$	$2$	$7.753$	$\Q(\sqrt{-14}) $	None		$2$	$0$	$0$	$-10$	$0$	$-150$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-5+2\beta )q^{3}+2q^{4}+(-28+\cdots)q^{6}+\cdots$
75.5.c.d	$75$	$5$	75.c	3.b	$2$	$2$	$2$	$7.753$	$\Q(\sqrt{-35}) $	None		$2$	$0$	$0$	$-3$	$0$	$144$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\beta )q^{2}+(-3+3\beta )q^{3}-19q^{4}+\cdots$
75.5.c.e	$75$	$5$	75.c	3.b	$2$	$2$	$2$	$7.753$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-15}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+7iq^{2}+9iq^{3}-33q^{4}-63q^{6}+\cdots$
75.5.c.f	$75$	$5$	75.c	3.b	$2$	$2$	$2$	$7.753$	$\Q(\sqrt{-35}) $	None		$2$	$0$	$0$	$3$	$0$	$-144$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\beta )q^{2}+3\beta q^{3}-19q^{4}+(54+\cdots)q^{6}+\cdots$

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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.