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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 (48 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
212.1.d.a	$212$	$1$	212.d	212.d	$2$	$1$	$1$	$0.106$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{12}+\cdots$
212.1.d.b	$212$	$1$	212.d	212.d	$2$	$1$	$1$	$0.106$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{12}+\cdots$
212.1.i.a	$212$	$1$	212.i	212.i	$26$	$12$	$1$	$0.106$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$		$1$		$q+\zeta_{26}^{6}q^{2}+\zeta_{26}^{12}q^{4}+(\zeta_{26}^{8}+\zeta_{26}^{10}+\cdots)q^{5}+\cdots$
212.2.a.a	$212$	$2$	212.a	1.a	$1$	$1$	$1$	$1.693$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}-2q^{9}+2q^{11}+\cdots$
212.2.a.b	$212$	$2$	212.a	1.a	$1$	$1$	$1$	$1.693$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
212.2.a.c	$212$	$2$	212.a	1.a	$1$	$3$	$3$	$1.693$	3.3.756.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{2}q^{5}+(2+\beta _{2})q^{7}+\cdots$
212.2.b.a	$212$	$2$	212.b	53.b	$2$	$4$	$4$	$1.693$	4.0.29952.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots$
212.2.f.a	$212$	$2$	212.f	212.f	$4$	$2$	$1$	$1.693$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1+i)q^{2}+2iq^{4}+(-1+i)q^{5}+\cdots$
212.2.f.b	$212$	$2$	212.f	212.f	$4$	$48$	$24$	$1.693$		$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
212.2.g.a	$212$	$2$	212.g	53.d	$13$	$60$	$5$	$1.693$		$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$-4$			$\mathrm{SU}(2)[C_{13}]$
212.2.j.a	$212$	$2$	212.j	53.e	$26$	$48$	$4$	$1.693$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{26}]$
212.2.k.a	$212$	$2$	212.k	212.k	$52$	$24$	$1$	$1.693$		$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$			$\mathrm{U}(1)[D_{52}]$
212.2.k.b	$212$	$2$	212.k	212.k	$52$	$576$	$24$	$1.693$		$_{}$	None	None		$4$	$0$	$-24$	$0$	$-52$	$0$			$\mathrm{SU}(2)[C_{52}]$
212.3.c.a	$212$	$3$	212.c	4.b	$2$	$52$	$52$	$5.777$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
212.3.d.a	$212$	$3$	212.d	212.d	$2$	$2$	$2$	$5.777$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}-4q^{4}+4iq^{5}-4iq^{8}-9q^{9}+\cdots$
212.3.d.b	$212$	$3$	212.d	212.d	$2$	$3$	$3$	$5.777$	3.3.5724.1	$_{}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$-6$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-\beta _{2}q^{3}+4q^{4}+2\beta _{2}q^{6}-8q^{8}+\cdots$
212.3.d.c	$212$	$3$	212.d	212.d	$2$	$3$	$3$	$5.777$	3.3.5724.1	$_{}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta _{2}q^{3}+4q^{4}+2\beta _{2}q^{6}+8q^{8}+\cdots$
212.3.d.d	$212$	$3$	212.d	212.d	$2$	$44$	$44$	$5.777$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
212.3.e.a	$212$	$3$	212.e	53.c	$4$	$18$	$9$	$5.777$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{15}q^{7}+(3\beta _{6}-\beta _{13}+\cdots)q^{9}+\cdots$
212.3.h.a	$212$	$3$	212.h	212.h	$26$	$24$	$2$	$5.777$		$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{26}]$
212.3.h.b	$212$	$3$	212.h	212.h	$26$	$600$	$50$	$5.777$		$_{}$	None	None		$4$	$0$	$-13$	$0$	$-26$	$0$			$\mathrm{SU}(2)[C_{26}]$
212.3.i.a	$212$	$3$	212.i	212.i	$26$	$624$	$52$	$5.777$		$_{}$	None	None		$4$	$0$	$-13$	$0$	$-26$	$0$			$\mathrm{SU}(2)[C_{26}]$
212.3.l.a	$212$	$3$	212.l	53.f	$52$	$216$	$9$	$5.777$		$_{}$	None	None		$2$	$0$	$0$	$2$	$8$	$0$			$\mathrm{SU}(2)[C_{52}]$
212.4.a.a	$212$	$4$	212.a	1.a	$1$	$5$	$5$	$12.508$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-9$	$-34$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+(-6+\cdots)q^{7}+\cdots$
212.4.a.b	$212$	$4$	212.a	1.a	$1$	$8$	$8$	$12.508$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$11$	$22$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{4})q^{5}+(3+\beta _{1}+\cdots)q^{7}+\cdots$
212.4.b.a	$212$	$4$	212.b	53.b	$2$	$14$	$14$	$12.508$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-12$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-1-\beta _{7})q^{7}+(-13+\cdots)q^{9}+\cdots$
212.4.f.a	$212$	$4$	212.f	212.f	$4$	$2$	$1$	$12.508$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-4$	$0$	$-26$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2-2i)q^{2}+8iq^{4}+(-13+13i)q^{5}+\cdots$
212.4.f.b	$212$	$4$	212.f	212.f	$4$	$156$	$78$	$12.508$		$_{}$	None	None		$4$	$0$	$0$	$0$	$20$	$0$			$\mathrm{SU}(2)[C_{4}]$
212.4.g.a	$212$	$4$	212.g	53.d	$13$	$156$	$13$	$12.508$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$-2$	$12$			$\mathrm{SU}(2)[C_{13}]$
212.4.j.a	$212$	$4$	212.j	53.e	$26$	$168$	$14$	$12.508$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{26}]$
212.4.k.a	$212$	$4$	212.k	212.k	$52$	$24$	$1$	$12.508$		$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$4$	$0$	$26$	$0$			$\mathrm{U}(1)[D_{52}]$
212.4.k.b	$212$	$4$	212.k	212.k	$52$	$1872$	$78$	$12.508$		$_{}$	None	None		$4$	$0$	$-26$	$0$	$-72$	$0$			$\mathrm{SU}(2)[C_{52}]$
212.5.e.a	$212$	$5$	212.e	53.c	$4$	$36$	$18$	$21.914$		$_{}$	None	None		$2$	$0$	$0$	$10$	$-30$	$0$			$\mathrm{SU}(2)[C_{4}]$
212.6.a.a	$212$	$6$	212.a	1.a	$1$	$9$	$9$	$34.001$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$11$	$-64$	$-146$	$+$	$2^{8}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-7+\beta _{6})q^{5}+(-2^{4}+\cdots)q^{7}+\cdots$
212.6.a.b	$212$	$6$	212.a	1.a	$1$	$12$	$12$	$34.001$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$11$	$36$	$246$	$-$	$2^{15}\cdot 3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(3+\beta _{1}-\beta _{2})q^{5}+(21+\cdots)q^{7}+\cdots$
212.6.b.a	$212$	$6$	212.b	53.b	$2$	$22$	$22$	$34.001$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-76$			$\mathrm{SU}(2)[C_{2}]$
212.7.e.a	$212$	$7$	212.e	53.c	$4$	$54$	$27$	$48.771$		$_{}$	None	None		$2$	$0$	$0$	$-32$	$122$	$0$			$\mathrm{SU}(2)[C_{4}]$
212.8.a.a	$212$	$8$	212.a	1.a	$1$	$14$	$14$	$66.226$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-13$	$-124$	$-698$	$-$	$2^{20}\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-9-\beta _{1}-\beta _{2})q^{5}+\cdots$
212.8.a.b	$212$	$8$	212.a	1.a	$1$	$17$	$17$	$66.226$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-13$	$376$	$2046$	$+$	$2^{28}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(22+\beta _{1}-\beta _{3})q^{5}+\cdots$
212.8.b.a	$212$	$8$	212.b	53.b	$2$	$32$	$32$	$66.226$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$1348$			$\mathrm{SU}(2)[C_{2}]$
212.9.e.a	$212$	$9$	212.e	53.c	$4$	$72$	$36$	$86.364$		$_{}$	None	None		$2$	$0$	$0$	$70$	$210$	$0$			$\mathrm{SU}(2)[C_{4}]$
212.10.a.a	$212$	$10$	212.a	1.a	$1$	$18$	$18$	$109.188$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-154$	$-2159$	$-8154$	$+$	$2^{34}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)$	$q+(-9+\beta _{1})q^{3}+(-120+\beta _{2})q^{5}+\cdots$
212.10.a.b	$212$	$10$	212.a	1.a	$1$	$21$	$21$	$109.188$		$_{}$	None	None	✓	$1$	$0$	$0$	$-154$	$341$	$11054$	$-$		$\mathrm{SU}(2)$
212.10.b.a	$212$	$10$	212.b	53.b	$2$	$40$	$40$	$109.188$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-9756$			$\mathrm{SU}(2)[C_{2}]$
212.11.e.a	$212$	$11$	212.e	53.c	$4$	$90$	$45$	$134.696$		$_{}$	None	None		$2$	$0$	$0$	$-62$	$-1748$	$0$			$\mathrm{SU}(2)[C_{4}]$
212.12.a.a	$212$	$12$	212.a	1.a	$1$	$22$	$22$	$162.889$		$_{}$	None	None	✓	$1$	$1$	$0$	$263$	$-594$	$-100778$	$-$		$\mathrm{SU}(2)$
212.12.a.b	$212$	$12$	212.a	1.a	$1$	$25$	$25$	$162.889$		$_{}$	None	None	✓	$1$	$0$	$0$	$263$	$11906$	$33678$	$+$		$\mathrm{SU}(2)$
212.12.b.a	$212$	$12$	212.b	53.b	$2$	$50$	$50$	$162.889$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$31508$			$\mathrm{SU}(2)[C_{2}]$

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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.