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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 1912 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$-4$	$-6$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
25.2.d.a	$25$	$2$	25.d	25.d	$5$	$4$	$1$	$0.200$	$\Q(\zeta_{10})$	None		$2$	$0$	$-2$	$-1$	$-5$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
31.2.d.a	$31$	$2$	31.d	31.d	$5$	$4$	$1$	$0.248$	$\Q(\zeta_{10})$	None		$2$	$0$	$-3$	$1$	$-6$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
33.2.e.a	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	$\Q(\zeta_{10})$	None		$2$	$0$	$-3$	$-1$	$-1$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots$
33.2.e.b	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$-3$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots$
41.2.d.a	$41$	$2$	41.d	41.d	$5$	$8$	$2$	$0.327$	8.0.13140625.1	None		$2$	$0$	$-1$	$-6$	$3$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}-\beta _{7})q^{2}+(-1+\beta _{5})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
44.2.e.a	$44$	$2$	44.e	11.c	$5$	$4$	$1$	$0.351$	$\Q(\zeta_{10})$	None		$2$	$0$	$0$	$-1$	$3$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{3}+(1-\zeta_{10}^{3})q^{5}+\cdots$
50.2.d.a	$50$	$2$	50.d	25.d	$5$	$4$	$1$	$0.399$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$-1$	$5$	$-12$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots$
50.2.d.b	$50$	$2$	50.d	25.d	$5$	$8$	$2$	$0.399$	8.0.58140625.2	None		$2$	$0$	$-2$	$-3$	$0$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{2}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+\cdots$
55.2.g.a	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.159390625.1	None		$2$	$0$	$-4$	$1$	$-2$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
55.2.g.b	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.13140625.1	None		$2$	$0$	$-2$	$-5$	$2$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
61.2.e.a	$61$	$2$	61.e	61.e	$5$	$12$	$3$	$0.487$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-2$	$-1$	$-5$	$-10$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{2}+(\beta _{8}+\beta _{10})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
62.2.d.a	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.511890625.1	None		$2$	$0$	$-2$	$-4$	$-4$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
62.2.d.b	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.1903140625.1	None		$2$	$0$	$2$	$-2$	$0$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
66.2.e.a	$66$	$2$	66.e	11.c	$5$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$8$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(2+\cdots)q^{5}+\cdots$
66.2.e.b	$66$	$2$	66.e	11.c	$5$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$-1$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-2+\cdots)q^{5}+\cdots$
71.2.c.a	$71$	$2$	71.c	71.c	$5$	$20$	$5$	$0.567$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-6$	$-1$	$-1$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{14}q^{2}+\beta _{17}q^{3}+(-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
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		$2$	$0$	$0$	$3$	$-6$	$-12$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots$
77.2.f.a	$77$	$2$	77.f	11.c	$5$	$8$	$2$	$0.615$	8.0.159390625.1	None		$2$	$0$	$-1$	$-4$	$3$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
77.2.f.b	$77$	$2$	77.f	11.c	$5$	$16$	$4$	$0.615$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-3$	$-2$	$-5$	$-4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}-\beta _{6})q^{2}+(\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots$
11.4.c.a	$11$	$4$	11.c	11.c	$5$	$8$	$2$	$0.649$	8.0.$\cdots$.1	None		$2$	$0$	$-7$	$-3$	$-7$	$-35$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots$
82.2.d.a	$82$	$2$	82.d	41.d	$5$	$4$	$1$	$0.655$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$6$	$4$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
82.2.d.b	$82$	$2$	82.d	41.d	$5$	$4$	$1$	$0.655$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$2$	$2$	$4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
82.2.d.c	$82$	$2$	82.d	41.d	$5$	$8$	$2$	$0.655$	8.0.123765625.1	None		$2$	$0$	$-2$	$-10$	$-10$	$4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(-2-\beta _{3}+\beta _{4}-\beta _{7})q^{3}+\cdots$
88.2.i.a	$88$	$2$	88.i	11.c	$5$	$4$	$1$	$0.703$	$\Q(\zeta_{10})$	None		$2$	$0$	$0$	$3$	$3$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10})q^{3}+(1-\zeta_{10}^{3})q^{5}+(-\zeta_{10}+\cdots)q^{7}+\cdots$
88.2.i.b	$88$	$2$	88.i	11.c	$5$	$8$	$2$	$0.703$	8.0.682515625.5	None		$2$	$0$	$0$	$-1$	$-3$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
93.2.f.a	$93$	$2$	93.f	31.d	$5$	$8$	$2$	$0.743$	$\Q(\zeta_{15})$	None		$2$	$0$	$3$	$2$	$-6$	$9$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{15}+\zeta_{15}^{3})q^{2}+(1+\zeta_{15}^{2}+\cdots)q^{3}+\cdots$
93.2.f.b	$93$	$2$	93.f	31.d	$5$	$16$	$4$	$0.743$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-3$	$-4$	$6$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{8}-\beta _{9}+\cdots)q^{4}+\cdots$
99.2.f.a	$99$	$2$	99.f	11.c	$5$	$4$	$1$	$0.791$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$0$	$3$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
99.2.f.b	$99$	$2$	99.f	11.c	$5$	$4$	$1$	$0.791$	$\Q(\zeta_{10})$	None		$2$	$0$	$3$	$0$	$1$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(1-2\zeta_{10}+\cdots)q^{5}+\cdots$
99.2.f.c	$99$	$2$	99.f	11.c	$5$	$8$	$2$	$0.791$	8.0.484000000.9	None		$4$	$0$	$0$	$0$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{2}+(1+2\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+\beta _{7})q^{5}+\cdots$
100.2.g.a	$100$	$2$	100.g	25.d	$5$	$12$	$3$	$0.799$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$2$	$-4$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{3}+(-1-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$
101.2.d.a	$101$	$2$	101.d	101.d	$5$	$28$	$7$	$0.806$		None		$2$	$0$	$-2$	$-3$	$5$	$3$		$\mathrm{SU}(2)[C_{5}]$
110.2.g.a	$110$	$2$	110.g	11.c	$5$	$4$	$1$	$0.878$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$4$	$1$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
110.2.g.b	$110$	$2$	110.g	11.c	$5$	$4$	$1$	$0.878$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$4$	$1$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots$
110.2.g.c	$110$	$2$	110.g	11.c	$5$	$8$	$2$	$0.878$	8.0.682515625.5	None		$2$	$0$	$2$	$-4$	$-2$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
121.2.c.a	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None		$4$	$0$	$-2$	$1$	$-1$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
121.2.c.b	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None		$4$	$0$	$-1$	$-2$	$-1$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
121.2.c.c	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	$\Q(\sqrt{-11}) $		$8$	$0$	$0$	$1$	$3$	$0$	$1$	$\mathrm{U}(1)[D_{5}]$	$q-\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+3\zeta_{10}q^{5}+\cdots$
121.2.c.d	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None		$4$	$0$	$1$	$-2$	$-1$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots$
121.2.c.e	$121$	$2$	121.c	11.c	$5$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	None		$4$	$0$	$2$	$1$	$-1$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots$
122.2.e.a	$122$	$2$	122.e	61.e	$5$	$12$	$3$	$0.974$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$-4$	$-6$	$10$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots$
122.2.e.b	$122$	$2$	122.e	61.e	$5$	$16$	$4$	$0.974$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$2$	$3$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{5}-\beta _{6}-\beta _{8})q^{2}-\beta _{3}q^{3}+\cdots$
123.2.g.a	$123$	$2$	123.g	41.d	$5$	$4$	$1$	$0.982$	$\Q(\zeta_{10})$	None		$2$	$1$	$-5$	$-4$	$-8$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
123.2.g.b	$123$	$2$	123.g	41.d	$5$	$12$	$3$	$0.982$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$4$	$-12$	$1$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{4}-\beta _{5})q^{2}-q^{3}+(-1+\cdots)q^{4}+\cdots$
123.2.g.c	$123$	$2$	123.g	41.d	$5$	$16$	$4$	$0.982$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-1$	$16$	$-1$	$-2$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{12}q^{2}+q^{3}+(-1+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
124.2.f.a	$124$	$2$	124.f	31.d	$5$	$4$	$1$	$0.990$	$\Q(\zeta_{10})$	None		$2$	$0$	$0$	$-3$	$8$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}^{3})q^{3}+2q^{5}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
124.2.f.b	$124$	$2$	124.f	31.d	$5$	$4$	$1$	$0.990$	$\Q(\zeta_{10})$	None		$2$	$0$	$0$	$5$	$-6$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots$

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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.