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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 242 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
25.2.d.a	$25$	$2$	25.d	25.d	$5$	$4$	$1$	$0.200$	$\Q(\zeta_{10})$	None		$2$	$0$	$-2$	$-1$	$-5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
25.2.e.a	$25$	$2$	25.e	25.e	$10$	$8$	$2$	$0.200$	8.0.58140625.2	None		$2$	$0$	$-5$	$-5$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots$
25.3.c.a	$25$	$3$	25.c	5.c	$4$	$4$	$2$	$0.681$	$\Q(i, \sqrt{6})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots$
25.3.f.a	$25$	$3$	25.f	25.f	$20$	$32$	$4$	$0.681$		None		$2$	$0$	$-10$	$-10$	$-10$	$-10$			$\mathrm{SU}(2)[C_{20}]$
25.4.a.a	$25$	$4$	25.a	1.a	$1$	$1$	$1$	$1.475$	$\Q$	None	✓	$1$	$1$	$-1$	$-7$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots$
25.4.a.b	$25$	$4$	25.a	1.a	$1$	$1$	$1$	$1.475$	$\Q$	None	✓	$1$	$0$	$1$	$7$	$0$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots$
25.4.a.c	$25$	$4$	25.a	1.a	$1$	$1$	$1$	$1.475$	$\Q$	None	✓	$1$	$0$	$4$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots$
25.4.b.a	$25$	$4$	25.b	5.b	$2$	$2$	$2$	$1.475$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+iq^{3}-8q^{4}-8q^{6}-3iq^{7}+\cdots$
25.4.b.b	$25$	$4$	25.b	5.b	$2$	$2$	$2$	$1.475$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-7iq^{3}+7q^{4}+7q^{6}+6iq^{7}+\cdots$
25.4.d.a	$25$	$4$	25.d	25.d	$5$	$28$	$7$	$1.475$		None		$2$	$0$	$-1$	$-7$	$-20$	$-16$			$\mathrm{SU}(2)[C_{5}]$
25.4.e.a	$25$	$4$	25.e	25.e	$10$	$24$	$6$	$1.475$		None		$2$	$0$	$-5$	$-5$	$15$	$0$			$\mathrm{SU}(2)[C_{10}]$
25.5.c.a	$25$	$5$	25.c	5.c	$4$	$2$	$1$	$2.584$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$12$	$0$	$52$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+(6-6i)q^{3}-14iq^{4}+\cdots$
25.5.c.b	$25$	$5$	25.c	5.c	$4$	$4$	$2$	$2.584$	$\Q(i, \sqrt{6})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+3\beta _{1}q^{2}+7\beta _{3}q^{3}+11\beta _{2}q^{4}-63q^{6}+\cdots$
25.5.c.c	$25$	$5$	25.c	5.c	$4$	$4$	$2$	$2.584$	$\Q(i, \sqrt{21})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+42q^{6}+\cdots$
25.5.f.a	$25$	$5$	25.f	25.f	$20$	$72$	$9$	$2.584$		None		$2$	$0$	$-8$	$2$	$-50$	$42$			$\mathrm{SU}(2)[C_{20}]$
25.6.a.a	$25$	$6$	25.a	1.a	$1$	$1$	$1$	$4.010$	$\Q$	None	✓	$1$	$1$	$-2$	$4$	$0$	$-192$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{3}-28q^{4}-8q^{6}-192q^{7}+\cdots$
25.6.a.b	$25$	$6$	25.a	1.a	$1$	$2$	$2$	$4.010$	$\Q(\sqrt{241}) $	None	✓	$1$	$1$	$-5$	$-20$	$0$	$-200$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+(-11+2\beta )q^{3}+(2^{5}+\cdots)q^{4}+\cdots$
25.6.a.c	$25$	$6$	25.a	1.a	$1$	$2$	$2$	$4.010$	$\Q(\sqrt{11}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{2}+3\beta q^{3}+12q^{4}+132q^{6}+\cdots$
25.6.a.d	$25$	$6$	25.a	1.a	$1$	$2$	$2$	$4.010$	$\Q(\sqrt{241}) $	None	✓	$1$	$0$	$5$	$20$	$0$	$200$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{2}+(9+2\beta )q^{3}+(37-5\beta )q^{4}+\cdots$
25.6.b.a	$25$	$6$	25.b	5.b	$2$	$2$	$2$	$4.010$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}+28q^{4}-8q^{6}+96iq^{7}+\cdots$
25.6.b.b	$25$	$6$	25.b	5.b	$2$	$4$	$4$	$4.010$	$\Q(i, \sqrt{241})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+\cdots$
25.6.d.a	$25$	$6$	25.d	25.d	$5$	$44$	$11$	$4.010$		None		$2$	$0$	$-7$	$-1$	$115$	$-202$			$\mathrm{SU}(2)[C_{5}]$
25.6.e.a	$25$	$6$	25.e	25.e	$10$	$48$	$12$	$4.010$		None		$2$	$0$	$-5$	$-5$	$-60$	$0$			$\mathrm{SU}(2)[C_{10}]$
25.7.c.a	$25$	$7$	25.c	5.c	$4$	$2$	$1$	$5.751$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-6$	$66$	$0$	$414$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-3-3i)q^{2}+(33-33i)q^{3}-46iq^{4}+\cdots$
25.7.c.b	$25$	$7$	25.c	5.c	$4$	$2$	$1$	$5.751$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$6$	$-66$	$0$	$-414$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(3+3i)q^{2}+(-33+33i)q^{3}-46iq^{4}+\cdots$
25.7.c.c	$25$	$7$	25.c	5.c	$4$	$4$	$2$	$5.751$	$\Q(i, \sqrt{201})$	None		$2$	$0$	$10$	$-30$	$0$	$-550$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(3-3\beta _{1}+\beta _{3})q^{2}+(-8-7\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
25.7.c.d	$25$	$7$	25.c	5.c	$4$	$8$	$4$	$5.751$	8.0.$\cdots$.23	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{2}+\beta _{3})q^{2}+(4\beta _{4}+3\beta _{5})q^{3}+(22\beta _{1}+\cdots)q^{4}+\cdots$
25.7.f.a	$25$	$7$	25.f	25.f	$20$	$112$	$14$	$5.751$		None		$2$	$0$	$0$	$-40$	$60$	$-560$			$\mathrm{SU}(2)[C_{20}]$
25.8.a.a	$25$	$8$	25.a	1.a	$1$	$1$	$1$	$7.810$	$\Q$	None	✓	$1$	$0$	$14$	$48$	$0$	$1644$	$+$	$1$	$\mathrm{SU}(2)$	$q+14q^{2}+48q^{3}+68q^{4}+672q^{6}+\cdots$
25.8.a.b	$25$	$8$	25.a	1.a	$1$	$2$	$2$	$7.810$	$\Q(\sqrt{19}) $	None	✓	$1$	$0$	$-20$	$-20$	$0$	$100$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-10+\beta )q^{2}+(-10-8\beta )q^{3}+(48+\cdots)q^{4}+\cdots$
25.8.a.c	$25$	$8$	25.a	1.a	$1$	$2$	$2$	$7.810$	$\Q(\sqrt{649}) $	None	✓	$1$	$1$	$-15$	$-40$	$0$	$600$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-7-\beta )q^{2}+(-19-2\beta )q^{3}+(83+\cdots)q^{4}+\cdots$
25.8.a.d	$25$	$8$	25.a	1.a	$1$	$2$	$2$	$7.810$	$\Q(\sqrt{29}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3\beta q^{3}-12q^{4}-348q^{6}+\cdots$
25.8.a.e	$25$	$8$	25.a	1.a	$1$	$2$	$2$	$7.810$	$\Q(\sqrt{649}) $	None	✓	$1$	$0$	$15$	$40$	$0$	$-600$	$+$	$1$	$\mathrm{SU}(2)$	$q+(8-\beta )q^{2}+(21-2\beta )q^{3}+(98-15\beta )q^{4}+\cdots$
25.8.b.a	$25$	$8$	25.b	5.b	$2$	$2$	$2$	$7.810$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+7iq^{2}-24iq^{3}-68q^{4}+672q^{6}+\cdots$
25.8.b.b	$25$	$8$	25.b	5.b	$2$	$4$	$4$	$7.810$	$\Q(i, \sqrt{649})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+2\beta _{2})q^{2}+(2\beta _{1}-5\beta _{2})q^{3}+\cdots$
25.8.b.c	$25$	$8$	25.b	5.b	$2$	$4$	$4$	$7.810$	$\Q(i, \sqrt{19})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}+8\beta _{3})q^{3}+(-48+\cdots)q^{4}+\cdots$
25.8.d.a	$25$	$8$	25.d	25.d	$5$	$68$	$17$	$7.810$		None		$2$	$0$	$-11$	$23$	$475$	$1734$			$\mathrm{SU}(2)[C_{5}]$
25.8.e.a	$25$	$8$	25.e	25.e	$10$	$64$	$16$	$7.810$		None		$2$	$0$	$-5$	$-5$	$-510$	$0$			$\mathrm{SU}(2)[C_{10}]$
25.9.c.a	$25$	$9$	25.c	5.c	$4$	$4$	$2$	$10.184$	$\Q(i, \sqrt{141})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+282q^{6}+\cdots$
25.9.c.b	$25$	$9$	25.c	5.c	$4$	$6$	$3$	$10.184$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$2$	$72$	$0$	$2352$		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+(12+12\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots$
25.9.c.c	$25$	$9$	25.c	5.c	$4$	$12$	$6$	$10.184$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3^{6}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+(281\beta _{1}+\cdots)q^{4}+\cdots$
25.9.f.a	$25$	$9$	25.f	25.f	$20$	$152$	$19$	$10.184$		None		$2$	$0$	$-8$	$62$	$-230$	$2342$			$\mathrm{SU}(2)[C_{20}]$
25.10.a.a	$25$	$10$	25.a	1.a	$1$	$1$	$1$	$12.876$	$\Q$	None	✓	$1$	$1$	$8$	$114$	$0$	$-4242$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{2}+114q^{3}-448q^{4}+912q^{6}+\cdots$
25.10.a.b	$25$	$10$	25.a	1.a	$1$	$2$	$2$	$12.876$	$\Q(\sqrt{1009}) $	None	✓	$1$	$1$	$10$	$-260$	$0$	$-1700$	$+$	$2$	$\mathrm{SU}(2)$	$q+(5-\beta )q^{2}+(-130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots$
25.10.a.c	$25$	$10$	25.a	1.a	$1$	$3$	$3$	$12.876$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$1$	$-33$	$-89$	$0$	$-5258$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	$q+(-11-\beta _{1})q^{2}+(-30-2\beta _{1}+\beta _{2})q^{3}+\cdots$
25.10.a.d	$25$	$10$	25.a	1.a	$1$	$3$	$3$	$12.876$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$0$	$33$	$89$	$0$	$5258$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q+(11+\beta _{1})q^{2}+(30+2\beta _{1}-\beta _{2})q^{3}+\cdots$
25.10.a.e	$25$	$10$	25.a	1.a	$1$	$4$	$4$	$12.876$	4.4.49740556.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(342-\beta _{3})q^{4}+\cdots$
25.10.b.a	$25$	$10$	25.b	5.b	$2$	$2$	$2$	$12.876$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+4iq^{2}-57iq^{3}+448q^{4}+912q^{6}+\cdots$
25.10.b.b	$25$	$10$	25.b	5.b	$2$	$4$	$4$	$12.876$	$\Q(i, \sqrt{1009})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}+14\beta _{2}+\cdots)q^{3}+\cdots$
25.10.b.c	$25$	$10$	25.b	5.b	$2$	$6$	$6$	$12.876$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-2\beta _{2}-\beta _{4})q^{3}+(-114+\cdots)q^{4}+\cdots$

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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.