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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 63 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
213.2.a.a	$213$	$2$	213.a	1.a	$1$	$1$	$1$	$1.701$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots$
213.2.a.b	$213$	$2$	213.a	1.a	$1$	$2$	$2$	$1.701$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-3$	$2$	$-5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-3+\cdots)q^{5}+\cdots$
213.2.a.c	$213$	$2$	213.a	1.a	$1$	$2$	$2$	$1.701$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$-2$	$1$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{5}+\cdots$
213.2.a.d	$213$	$2$	213.a	1.a	$1$	$2$	$2$	$1.701$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$1$	$2$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{4}-\beta q^{5}+\beta q^{6}+\cdots$
213.2.a.e	$213$	$2$	213.a	1.a	$1$	$4$	$4$	$1.701$	4.4.2225.1	None	✓	$1$	$0$	$3$	$-4$	$-3$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
213.2.b.a	$213$	$2$	213.b	213.b	$2$	$8$	$8$	$1.701$	8.0.$\cdots$.2	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{4}+\cdots)q^{3}+\cdots$
213.2.b.b	$213$	$2$	213.b	213.b	$2$	$14$	$14$	$1.701$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$\Q(\sqrt{-71}) $		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}-\beta _{9}q^{5}+\cdots$
213.2.e.a	$213$	$2$	213.e	71.c	$5$	$4$	$1$	$1.701$	$\Q(\zeta_{10})$	None		$2$	$0$	$3$	$1$	$-8$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
213.2.e.b	$213$	$2$	213.e	71.c	$5$	$20$	$5$	$1.701$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$5$	$10$	$-3$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(1-\beta _{5}+\beta _{11}-\beta _{14})q^{3}+\cdots$
213.2.e.c	$213$	$2$	213.e	71.c	$5$	$24$	$6$	$1.701$		None		$2$	$0$	$3$	$-6$	$-2$	$-4$			$\mathrm{SU}(2)[C_{5}]$
213.2.f.a	$213$	$2$	213.f	71.d	$7$	$36$	$6$	$1.701$		None		$2$	$0$	$-2$	$-6$	$-2$	$-4$			$\mathrm{SU}(2)[C_{7}]$
213.2.f.b	$213$	$2$	213.f	71.d	$7$	$36$	$6$	$1.701$		None		$2$	$0$	$-2$	$6$	$2$	$0$			$\mathrm{SU}(2)[C_{7}]$
213.2.i.a	$213$	$2$	213.i	213.i	$10$	$8$	$2$	$1.701$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$-4$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
213.2.i.b	$213$	$2$	213.i	213.i	$10$	$80$	$20$	$1.701$		None		$4$	$0$	$0$	$3$	$0$	$-20$			$\mathrm{SU}(2)[C_{10}]$
213.2.l.a	$213$	$2$	213.l	213.l	$14$	$132$	$22$	$1.701$		None		$4$	$0$	$0$	$-10$	$0$	$-14$			$\mathrm{SU}(2)[C_{14}]$
213.2.m.a	$213$	$2$	213.m	71.g	$35$	$144$	$6$	$1.701$		None		$2$	$0$	$-3$	$-6$	$-2$	$0$			$\mathrm{SU}(2)[C_{35}]$
213.2.m.b	$213$	$2$	213.m	71.g	$35$	$144$	$6$	$1.701$		None		$2$	$0$	$-3$	$6$	$2$	$4$			$\mathrm{SU}(2)[C_{35}]$
213.2.n.a	$213$	$2$	213.n	213.n	$70$	$528$	$22$	$1.701$		None		$4$	$0$	$0$	$-20$	$0$	$-46$			$\mathrm{SU}(2)[C_{70}]$
213.3.c.a	$213$	$3$	213.c	3.b	$2$	$4$	$4$	$5.804$	$\Q(\sqrt{-7}, \sqrt{-71})$	None		$2$	$0$	$0$	$-12$	$0$	$10$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-3q^{3}-3q^{4}+\beta _{1}q^{5}+3\beta _{2}q^{6}+\cdots$
213.3.c.b	$213$	$3$	213.c	3.b	$2$	$42$	$42$	$5.804$		None		$2$	$0$	$0$	$8$	$0$	$-14$			$\mathrm{SU}(2)[C_{2}]$
213.3.d.a	$213$	$3$	213.d	71.b	$2$	$24$	$24$	$5.804$		None		$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
213.3.g.a	$213$	$3$	213.g	71.e	$10$	$96$	$24$	$5.804$		None		$2$	$0$	$6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
213.3.h.a	$213$	$3$	213.h	213.h	$10$	$184$	$46$	$5.804$		None		$4$	$0$	$0$	$-1$	$0$	$-6$			$\mathrm{SU}(2)[C_{10}]$
213.3.j.a	$213$	$3$	213.j	71.f	$14$	$144$	$24$	$5.804$		None		$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
213.3.k.a	$213$	$3$	213.k	213.k	$14$	$276$	$46$	$5.804$		None		$4$	$0$	$0$	$-10$	$0$	$-10$			$\mathrm{SU}(2)[C_{14}]$
213.3.o.a	$213$	$3$	213.o	213.o	$70$	$1104$	$46$	$5.804$		None		$4$	$0$	$0$	$-20$	$0$	$-50$			$\mathrm{SU}(2)[C_{70}]$
213.3.p.a	$213$	$3$	213.p	71.h	$70$	$576$	$24$	$5.804$		None		$2$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{70}]$
213.4.a.a	$213$	$4$	213.a	1.a	$1$	$1$	$1$	$12.567$	$\Q$	None	✓	$1$	$0$	$5$	$-3$	$13$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}-3q^{3}+17q^{4}+13q^{5}-15q^{6}+\cdots$
213.4.a.b	$213$	$4$	213.a	1.a	$1$	$8$	$8$	$12.567$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-9$	$24$	$-32$	$-56$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+3q^{3}+(3+2\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots$
213.4.a.c	$213$	$4$	213.a	1.a	$1$	$8$	$8$	$12.567$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-5$	$-24$	$12$	$-42$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
213.4.a.d	$213$	$4$	213.a	1.a	$1$	$9$	$9$	$12.567$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-2$	$-27$	$-21$	$49$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-3+\cdots)q^{5}+\cdots$
213.4.a.e	$213$	$4$	213.a	1.a	$1$	$10$	$10$	$12.567$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$7$	$30$	$28$	$28$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
213.4.b.a	$213$	$4$	213.b	213.b	$2$	$14$	$14$	$12.567$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$\Q(\sqrt{-71}) $		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(-\beta _{5}+\beta _{8})q^{3}+(-8-3\beta _{6}+\cdots)q^{4}+\cdots$
213.4.b.b	$213$	$4$	213.b	213.b	$2$	$56$	$56$	$12.567$		None		$4$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
213.4.e.a	$213$	$4$	213.e	71.c	$5$	$72$	$18$	$12.567$		None		$2$	$0$	$-3$	$-54$	$4$	$28$			$\mathrm{SU}(2)[C_{5}]$
213.4.e.b	$213$	$4$	213.e	71.c	$5$	$72$	$18$	$12.567$		None		$2$	$0$	$-3$	$54$	$-4$	$0$			$\mathrm{SU}(2)[C_{5}]$
213.4.f.a	$213$	$4$	213.f	71.d	$7$	$108$	$18$	$12.567$		None		$2$	$0$	$2$	$-54$	$4$	$28$			$\mathrm{SU}(2)[C_{7}]$
213.4.f.b	$213$	$4$	213.f	71.d	$7$	$108$	$18$	$12.567$		None		$2$	$0$	$2$	$54$	$-4$	$0$			$\mathrm{SU}(2)[C_{7}]$
213.4.i.a	$213$	$4$	213.i	213.i	$10$	$280$	$70$	$12.567$		None		$4$	$0$	$0$	$-7$	$0$	$-10$			$\mathrm{SU}(2)[C_{10}]$
213.4.l.a	$213$	$4$	213.l	213.l	$14$	$420$	$70$	$12.567$		None		$4$	$0$	$0$	$5$	$0$	$-14$			$\mathrm{SU}(2)[C_{14}]$
213.4.m.a	$213$	$4$	213.m	71.g	$35$	$432$	$18$	$12.567$		None		$2$	$0$	$3$	$-54$	$4$	$0$			$\mathrm{SU}(2)[C_{35}]$
213.4.m.b	$213$	$4$	213.m	71.g	$35$	$432$	$18$	$12.567$		None		$2$	$0$	$3$	$54$	$-4$	$-28$			$\mathrm{SU}(2)[C_{35}]$
213.4.n.a	$213$	$4$	213.n	213.n	$70$	$1680$	$70$	$12.567$		None		$4$	$0$	$0$	$-35$	$0$	$-46$			$\mathrm{SU}(2)[C_{70}]$
213.5.c.a	$213$	$5$	213.c	3.b	$2$	$94$	$94$	$22.018$		None		$2$	$0$	$0$	$8$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
213.5.d.a	$213$	$5$	213.d	71.b	$2$	$48$	$48$	$22.018$		None		$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
213.6.a.a	$213$	$6$	213.a	1.a	$1$	$13$	$13$	$34.162$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$-11$	$117$	$-167$	$-156$	$+$	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+9q^{3}+(12-2\beta _{1}+\cdots)q^{4}+\cdots$
213.6.a.b	$213$	$6$	213.a	1.a	$1$	$14$	$14$	$34.162$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-9$	$-126$	$61$	$-294$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-9q^{3}+(15-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
213.6.a.c	$213$	$6$	213.a	1.a	$1$	$15$	$15$	$34.162$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$21$	$135$	$133$	$432$	$-$	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+9q^{3}+(2^{4}+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
213.6.a.d	$213$	$6$	213.a	1.a	$1$	$16$	$16$	$34.162$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$7$	$-144$	$-39$	$294$	$-$	$2^{9}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-9q^{3}+(18+\beta _{1}+\beta _{2})q^{4}+\cdots$
213.7.d.a	$213$	$7$	213.d	71.b	$2$	$72$	$72$	$49.002$		None		$2$	$0$	$20$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.