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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				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
197.2.a.a	$197$	$2$	197.a	1.a	$1$	$1$	$1$	$1.573$	$\Q$	None	✓	✓			197.2.a.a	$1$	$1$	$-2$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{7}-3q^{9}+4q^{11}+\cdots$
197.2.a.b	$197$	$2$	197.a	1.a	$1$	$5$	$5$	$1.573$	5.5.24217.1	None	✓	✓	✓		197.2.a.b	$1$	$1$	$0$	$-8$	$-4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
197.2.a.c	$197$	$2$	197.a	1.a	$1$	$10$	$10$	$1.573$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	197.2.a.c	$1$	$0$	$0$	$10$	$2$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
197.2.b.a	$197$	$2$	197.b	197.b	$2$	$16$	$16$	$1.573$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	197.2.b.a	$2$	$0$	$0$	$0$	$0$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$
197.2.d.a	$197$	$2$	197.d	197.d	$7$	$90$	$15$	$1.573$		None		✓	✓	✓	197.2.d.a	$2$	$0$	$-2$	$-5$	$1$	$-11$			$\mathrm{SU}(2)[C_{7}]$
197.2.e.a	$197$	$2$	197.e	197.e	$14$	$6$	$1$	$1.573$	$\Q(\zeta_{14})$	None		✓			197.2.e.a	$2$	$0$	$0$	$-7$	$7$	$-1$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-1-\zeta_{14}^{5})q^{3}+\cdots$
197.2.e.b	$197$	$2$	197.e	197.e	$14$	$90$	$15$	$1.573$		None		✓	✓		197.2.e.b	$2$	$0$	$-7$	$0$	$-14$	$6$			$\mathrm{SU}(2)[C_{14}]$
197.2.g.a	$197$	$2$	197.g	197.g	$49$	$630$	$15$	$1.573$		None		✓	✓	✓	197.2.g.a	$2$	$0$	$-42$	$-42$	$-42$	$-28$			$\mathrm{SU}(2)[C_{49}]$
197.2.h.a	$197$	$2$	197.h	197.h	$98$	$672$	$16$	$1.573$		None		✓	✓	✓	197.2.h.a	$2$	$0$	$-42$	$-42$	$-42$	$-56$			$\mathrm{SU}(2)[C_{98}]$
197.3.c.a	$197$	$3$	197.c	197.c	$4$	$64$	$32$	$5.368$		None		✓	✓	✓	197.3.c.a	$2$	$0$	$-2$	$-2$	$-10$	$0$			$\mathrm{SU}(2)[C_{4}]$
197.3.f.a	$197$	$3$	197.f	197.f	$28$	$384$	$32$	$5.368$		None		✓	✓	✓	197.3.f.a	$2$	$0$	$-12$	$-12$	$-4$	$-14$			$\mathrm{SU}(2)[C_{28}]$
197.3.i.a	$197$	$3$	197.i	197.i	$196$	$2688$	$32$	$5.368$		None		✓	✓	✓	197.3.i.a	$2$	$0$	$-84$	$-84$	$-84$	$-84$			$\mathrm{SU}(2)[C_{196}]$
197.4.a.a	$197$	$4$	197.a	1.a	$1$	$22$	$22$	$11.623$		None	✓	✓	✓	✓	197.4.a.a	$1$	$1$	$-6$	$-34$	$-31$	$-102$	$-$		$\mathrm{SU}(2)$
197.4.a.b	$197$	$4$	197.a	1.a	$1$	$27$	$27$	$11.623$		None	✓	✓	✓	✓	197.4.a.b	$1$	$0$	$4$	$32$	$29$	$122$	$+$		$\mathrm{SU}(2)$
197.4.b.a	$197$	$4$	197.b	197.b	$2$	$48$	$48$	$11.623$		None		✓	✓	✓	197.4.b.a	$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
197.4.d.a	$197$	$4$	197.d	197.d	$7$	$294$	$49$	$11.623$		None		✓	✓	✓	197.4.d.a	$2$	$0$	$-5$	$-5$	$-5$	$15$			$\mathrm{SU}(2)[C_{7}]$
197.4.e.a	$197$	$4$	197.e	197.e	$14$	$288$	$48$	$11.623$		None		✓	✓	✓	197.4.e.a	$2$	$0$	$-7$	$-7$	$-7$	$-53$			$\mathrm{SU}(2)[C_{14}]$
197.4.g.a	$197$	$4$	197.g	197.g	$49$	$2058$	$49$	$11.623$		None		✓	✓	✓	197.4.g.a	$2$	$0$	$-42$	$-42$	$-42$	$-84$			$\mathrm{SU}(2)[C_{49}]$
197.4.h.a	$197$	$4$	197.h	197.h	$98$	$2016$	$48$	$11.623$		None		✓	✓	✓	197.4.h.a	$2$	$0$	$-42$	$-42$	$-42$	$0$			$\mathrm{SU}(2)[C_{98}]$
197.6.a.a	$197$	$6$	197.a	1.a	$1$	$38$	$38$	$31.596$		None	✓	✓	✓	✓	197.6.a.a	$1$	$1$	$-8$	$-100$	$-154$	$-737$	$+$		$\mathrm{SU}(2)$
197.6.a.b	$197$	$6$	197.a	1.a	$1$	$43$	$43$	$31.596$		None	✓	✓	✓	✓	197.6.a.b	$1$	$0$	$12$	$98$	$146$	$831$	$-$		$\mathrm{SU}(2)$
197.6.b.a	$197$	$6$	197.b	197.b	$2$	$82$	$82$	$31.596$		None		✓	✓	✓	197.6.b.a	$2$	$0$	$0$	$0$	$0$	$-294$			$\mathrm{SU}(2)[C_{2}]$
197.8.a.a	$197$	$8$	197.a	1.a	$1$	$55$	$55$	$61.540$		None	✓	✓	✓	✓	197.8.a.a	$1$	$1$	$-24$	$-298$	$-946$	$-6017$	$-$		$\mathrm{SU}(2)$
197.8.a.b	$197$	$8$	197.a	1.a	$1$	$60$	$60$	$61.540$		None	✓	✓	✓	✓	197.8.a.b	$1$	$0$	$16$	$296$	$554$	$4959$	$+$		$\mathrm{SU}(2)$
197.10.a.a	$197$	$10$	197.a	1.a	$1$	$71$	$71$	$101.462$		None	✓	✓	✓	✓	197.10.a.a	$1$	$1$	$-32$	$-892$	$-2329$	$-37846$	$+$		$\mathrm{SU}(2)$
197.10.a.b	$197$	$10$	197.a	1.a	$1$	$76$	$76$	$101.462$		None	✓	✓	✓	✓	197.10.a.b	$1$	$0$	$48$	$890$	$5171$	$38986$	$-$		$\mathrm{SU}(2)$
197.12.a.a	$197$	$12$	197.a	1.a	$1$	$87$	$87$	$151.364$		None	✓	✓	✓	✓	197.12.a.a	$1$	$1$	$-96$	$-2926$	$-20896$	$-231933$	$-$		$\mathrm{SU}(2)$
197.12.a.b	$197$	$12$	197.a	1.a	$1$	$92$	$92$	$151.364$		None	✓	✓	✓	✓	197.12.a.b	$1$	$0$	$64$	$2420$	$16604$	$305891$	$+$		$\mathrm{SU}(2)$
197.14.a.a	$197$	$14$	197.a	1.a	$1$	$104$	$104$	$211.245$		None	✓	✓	✓	✓	197.14.a.a	$1$	$1$	$-128$	$-8020$	$-99004$	$-2084037$	$+$		$\mathrm{SU}(2)$
197.14.a.b	$197$	$14$	197.a	1.a	$1$	$109$	$109$	$211.245$		None	✓	✓	✓	✓	197.14.a.b	$1$	$0$	$192$	$8018$	$88496$	$1680731$	$-$		$\mathrm{SU}(2)$

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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.