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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 293 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
98.2.a.a	$98$	$2$	98.a	1.a	$1$	$1$	$1$	$0.783$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
98.2.a.b	$98$	$2$	98.a	1.a	$1$	$2$	$2$	$0.783$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots$
98.2.c.a	$98$	$2$	98.c	7.c	$3$	$2$	$1$	$0.783$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
98.2.c.b	$98$	$2$	98.c	7.c	$3$	$2$	$1$	$0.783$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
98.2.c.c	$98$	$2$	98.c	7.c	$3$	$4$	$2$	$0.783$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots$
98.2.e.a	$98$	$2$	98.e	49.e	$7$	$18$	$3$	$0.783$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$-3$	$3$	$-6$	$-7$		$7$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{13}q^{2}+(\beta _{1}-\beta _{14})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots$
98.2.e.b	$98$	$2$	98.e	49.e	$7$	$18$	$3$	$0.783$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$3$	$-5$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{9}q^{2}+\beta _{4}q^{3}+(-1-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
98.2.g.a	$98$	$2$	98.g	49.g	$21$	$24$	$2$	$0.783$		None		$2$	$0$	$-2$	$7$	$0$	$0$			$\mathrm{SU}(2)[C_{21}]$
98.2.g.b	$98$	$2$	98.g	49.g	$21$	$24$	$2$	$0.783$		None		$2$	$0$	$2$	$-7$	$0$	$0$			$\mathrm{SU}(2)[C_{21}]$
98.3.b.a	$98$	$3$	98.b	7.b	$2$	$4$	$4$	$2.670$	4.0.2048.2	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(2\beta _{1}+2\beta _{3})q^{3}+2q^{4}+(-4\beta _{1}+\cdots)q^{5}+\cdots$
98.3.b.b	$98$	$3$	98.b	7.b	$2$	$4$	$4$	$2.670$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
98.3.d.a	$98$	$3$	98.d	7.d	$6$	$4$	$2$	$2.670$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$6$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$
98.3.d.b	$98$	$3$	98.d	7.d	$6$	$8$	$4$	$2.670$	8.0.339738624.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+(2\beta _{1}+2\beta _{3})q^{3}+(-2-2\beta _{4}+\cdots)q^{4}+\cdots$
98.3.f.a	$98$	$3$	98.f	49.f	$14$	$48$	$8$	$2.670$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
98.3.h.a	$98$	$3$	98.h	49.h	$42$	$120$	$10$	$2.670$		None		$2$	$0$	$0$	$6$	$6$	$-8$			$\mathrm{SU}(2)[C_{42}]$
98.4.a.a	$98$	$4$	98.a	1.a	$1$	$1$	$1$	$5.782$	$\Q$	None	✓	$1$	$1$	$-2$	$-8$	$14$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-8q^{3}+4q^{4}+14q^{5}+2^{4}q^{6}+\cdots$
98.4.a.b	$98$	$4$	98.a	1.a	$1$	$1$	$1$	$5.782$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+4q^{4}+7q^{5}+2q^{6}+\cdots$
98.4.a.c	$98$	$4$	98.a	1.a	$1$	$1$	$1$	$5.782$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$-7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+4q^{4}-7q^{5}-2q^{6}+\cdots$
98.4.a.d	$98$	$4$	98.a	1.a	$1$	$1$	$1$	$5.782$	$\Q$	None	✓	$1$	$1$	$2$	$-5$	$-9$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-5q^{3}+4q^{4}-9q^{5}-10q^{6}+\cdots$
98.4.a.e	$98$	$4$	98.a	1.a	$1$	$1$	$1$	$5.782$	$\Q$	None	✓	$1$	$0$	$2$	$2$	$12$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+4q^{4}+12q^{5}+4q^{6}+\cdots$
98.4.a.f	$98$	$4$	98.a	1.a	$1$	$1$	$1$	$5.782$	$\Q$	None	✓	$1$	$0$	$2$	$5$	$9$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+5q^{3}+4q^{4}+9q^{5}+10q^{6}+\cdots$
98.4.a.g	$98$	$4$	98.a	1.a	$1$	$2$	$2$	$5.782$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+5\beta q^{3}+4q^{4}+14\beta q^{5}-10\beta q^{6}+\cdots$
98.4.a.h	$98$	$4$	98.a	1.a	$1$	$2$	$2$	$5.782$	$\Q(\sqrt{22}) $	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta q^{3}+4q^{4}-\beta q^{5}+2\beta q^{6}+\cdots$
98.4.c.a	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-5$	$-9$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
98.4.c.b	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-2$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
98.4.c.c	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$2$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
98.4.c.d	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-8$	$14$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
98.4.c.e	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-1$	$7$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
98.4.c.f	$98$	$4$	98.c	7.c	$3$	$2$	$1$	$5.782$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$8$	$-14$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(8-8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
98.4.c.g	$98$	$4$	98.c	7.c	$3$	$4$	$2$	$5.782$	$\Q(\sqrt{-3}, \sqrt{22})$	None		$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-2\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots$
98.4.c.h	$98$	$4$	98.c	7.c	$3$	$4$	$2$	$5.782$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2+2\beta _{2})q^{2}+(5\beta _{1}+5\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots$
98.4.e.a	$98$	$4$	98.e	49.e	$7$	$42$	$7$	$5.782$		None		$2$	$0$	$-14$	$-5$	$12$	$-7$			$\mathrm{SU}(2)[C_{7}]$
98.4.e.b	$98$	$4$	98.e	49.e	$7$	$42$	$7$	$5.782$		None		$2$	$0$	$14$	$-1$	$14$	$7$			$\mathrm{SU}(2)[C_{7}]$
98.4.g.a	$98$	$4$	98.g	49.g	$21$	$84$	$7$	$5.782$		None		$2$	$0$	$-14$	$-8$	$7$	$20$			$\mathrm{SU}(2)[C_{21}]$
98.4.g.b	$98$	$4$	98.g	49.g	$21$	$84$	$7$	$5.782$		None		$2$	$0$	$14$	$2$	$-9$	$28$			$\mathrm{SU}(2)[C_{21}]$
98.5.b.a	$98$	$5$	98.b	7.b	$2$	$4$	$4$	$10.130$	4.0.2048.2	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{2}q^{2}+(-4\beta _{1}-7\beta _{3})q^{3}+8q^{4}+\cdots$
98.5.b.b	$98$	$5$	98.b	7.b	$2$	$4$	$4$	$10.130$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-3\beta _{2}-2\beta _{3})q^{3}+8q^{4}+\cdots$
98.5.b.c	$98$	$5$	98.b	7.b	$2$	$4$	$4$	$10.130$	4.0.2048.2	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{2}q^{2}+3\beta _{1}q^{3}+8q^{4}+(19\beta _{1}+\cdots)q^{5}+\cdots$
98.5.d.a	$98$	$5$	98.d	7.d	$6$	$4$	$2$	$10.130$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$18$	$-54$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(6-2\beta _{1}+3\beta _{2}+2\beta _{3})q^{3}+\cdots$
98.5.d.b	$98$	$5$	98.d	7.d	$6$	$8$	$4$	$10.130$	8.0.339738624.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\beta _{6}q^{2}+3\beta _{3}q^{3}+(-8-8\beta _{4})q^{4}+\cdots$
98.5.d.c	$98$	$5$	98.d	7.d	$6$	$8$	$4$	$10.130$	8.0.339738624.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\beta _{6}q^{2}+(4\beta _{1}+7\beta _{3})q^{3}+(-8-8\beta _{4}+\cdots)q^{4}+\cdots$
98.5.d.d	$98$	$5$	98.d	7.d	$6$	$8$	$4$	$10.130$	8.0.$\cdots$.28	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{5}-\beta _{6})q^{2}+(\beta _{3}-\beta _{4})q^{3}+(-8+\cdots)q^{4}+\cdots$
98.5.f.a	$98$	$5$	98.f	49.f	$14$	$120$	$20$	$10.130$		None		$2$	$0$	$0$	$0$	$0$	$76$			$\mathrm{SU}(2)[C_{14}]$
98.5.h.a	$98$	$5$	98.h	49.h	$42$	$216$	$18$	$10.130$		None		$2$	$0$	$0$	$18$	$-54$	$28$			$\mathrm{SU}(2)[C_{42}]$
98.6.a.a	$98$	$6$	98.a	1.a	$1$	$1$	$1$	$15.718$	$\Q$	None	✓	$1$	$0$	$-4$	$-10$	$-84$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-10q^{3}+2^{4}q^{4}-84q^{5}+40q^{6}+\cdots$
98.6.a.b	$98$	$6$	98.a	1.a	$1$	$1$	$1$	$15.718$	$\Q$	None	✓	$1$	$1$	$4$	$-8$	$-10$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-8q^{3}+2^{4}q^{4}-10q^{5}-2^{5}q^{6}+\cdots$
98.6.a.c	$98$	$6$	98.a	1.a	$1$	$2$	$2$	$15.718$	$\Q(\sqrt{130}) $	None	✓	$1$	$1$	$-8$	$-14$	$-42$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(-7+\beta )q^{3}+2^{4}q^{4}-21q^{5}+\cdots$
98.6.a.d	$98$	$6$	98.a	1.a	$1$	$2$	$2$	$15.718$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-8$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+6\beta q^{3}+2^{4}q^{4}-7\beta q^{5}-24\beta q^{6}+\cdots$
98.6.a.e	$98$	$6$	98.a	1.a	$1$	$2$	$2$	$15.718$	$\Q(\sqrt{46}) $	None	✓	$2$	$0$	$-8$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+\beta q^{3}+2^{4}q^{4}-7\beta q^{5}-4\beta q^{6}+\cdots$
98.6.a.f	$98$	$6$	98.a	1.a	$1$	$2$	$2$	$15.718$	$\Q(\sqrt{130}) $	None	✓	$1$	$0$	$-8$	$14$	$42$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(7+\beta )q^{3}+2^{4}q^{4}+21q^{5}+\cdots$

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Elliptic curves over $\Q$
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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.