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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 (1-50 of 97 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.1.d.a	$2$	$0$	$-1$	$-1$	$-1$	$2$		$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.1.d.a	$2$	$0$	$-1$	$1$	$1$	$-2$		$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.2.a.a	$119$	$2$	119.a	1.a	$1$	$4$	$4$	$0.950$	4.4.9301.1	$_{}$	None	None	✓	✓	✓	✓	119.2.a.a	$1$	$0$	$-1$	$2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
119.2.a.b	$119$	$2$	119.a	1.a	$1$	$5$	$5$	$0.950$	5.5.453749.1	$_{}$	None	None	✓	✓	✓	✓	119.2.a.b	$1$	$0$	$2$	$-2$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots$
119.2.b.a	$119$	$2$	119.b	17.b	$2$	$10$	$10$	$0.950$	10.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	119.2.b.a	$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
119.2.e.a	$119$	$2$	119.e	7.c	$3$	$6$	$3$	$0.950$	6.0.64827.1	$_{}$	None	None		✓			119.2.e.a	$2$	$0$	$1$	$-1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
119.2.e.b	$119$	$2$	119.e	7.c	$3$	$14$	$7$	$0.950$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		119.2.e.b	$2$	$0$	$-3$	$-1$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(\beta _{8}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots$
119.2.g.a	$119$	$2$	119.g	17.c	$4$	$20$	$10$	$0.950$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓	✓	119.2.g.a	$2$	$0$	$0$	$-4$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{17}q^{3}+(-2+\beta _{12}+\beta _{13}+\cdots)q^{4}+\cdots$
119.2.j.a	$119$	$2$	119.j	119.j	$6$	$20$	$10$	$0.950$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓	✓	119.2.j.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{15}q^{2}-\beta _{1}q^{3}+(-1+\beta _{11}+\beta _{14}+\cdots)q^{4}+\cdots$
119.2.k.a	$119$	$2$	119.k	17.d	$8$	$32$	$8$	$0.950$		$_{}$	None	None		✓	✓	✓	119.2.k.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
119.2.n.a	$119$	$2$	119.n	119.n	$12$	$8$	$2$	$0.950$	8.0.303595776.1	$_{}$	None	None		✓			119.2.n.a	$4$	$0$	$0$	$-2$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+\beta _{4}q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
119.2.n.b	$119$	$2$	119.n	119.n	$12$	$32$	$8$	$0.950$		$_{}$	None	None		✓	✓		119.2.n.b	$4$	$0$	$0$	$0$	$-8$	$-6$			$\mathrm{SU}(2)[C_{12}]$
119.2.p.a	$119$	$2$	119.p	119.p	$16$	$80$	$10$	$0.950$		$_{}$	None	None		✓	✓	✓	119.2.p.a	$4$	$0$	$-16$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{16}]$
119.2.q.a	$119$	$2$	119.q	119.q	$24$	$80$	$10$	$0.950$		$_{}$	None	None		✓	✓	✓	119.2.q.a	$4$	$0$	$-4$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{24}]$
119.2.s.a	$119$	$2$	119.s	119.s	$48$	$160$	$10$	$0.950$		$_{}$	None	None		✓	✓	✓	119.2.s.a	$4$	$0$	$-8$	$-24$	$-24$	$-16$			$\mathrm{SU}(2)[C_{48}]$
119.3.c.a	$119$	$3$	119.c	7.b	$2$	$20$	$20$	$3.243$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓	✓	119.3.c.a	$2$	$0$	$2$	$0$	$0$	$18$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+\beta _{1}q^{3}+(1-\beta _{4})q^{4}+\beta _{12}q^{5}+\cdots$
119.3.d.a	$119$	$3$	119.d	119.d	$2$	$5$	$5$	$3.243$	5.5.44253125.1	$_{}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.3.d.a	$2$	$0$	$0$	$0$	$0$	$35$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{3})q^{3}+(4+\beta _{1}+\cdots)q^{4}+\cdots$
119.3.d.b	$119$	$3$	119.d	119.d	$2$	$5$	$5$	$3.243$	5.5.44253125.1	$_{}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.3.d.a	$2$	$0$	$0$	$0$	$0$	$-35$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(4+\beta _{1}+\beta _{4})q^{4}+\cdots$
119.3.d.c	$119$	$3$	119.d	119.d	$2$	$12$	$12$	$3.243$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		119.3.d.c	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{9}q^{3}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
119.3.f.a	$119$	$3$	119.f	119.f	$4$	$44$	$22$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.f.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
119.3.h.a	$119$	$3$	119.h	119.h	$6$	$44$	$22$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.h.a	$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
119.3.i.a	$119$	$3$	119.i	7.d	$6$	$44$	$22$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.i.a	$2$	$0$	$-2$	$-6$	$0$	$-10$			$\mathrm{SU}(2)[C_{6}]$
119.3.l.a	$119$	$3$	119.l	119.l	$8$	$88$	$22$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.l.a	$4$	$0$	$-8$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
119.3.m.a	$119$	$3$	119.m	119.m	$12$	$88$	$22$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.m.a	$4$	$0$	$0$	$-6$	$0$	$2$			$\mathrm{SU}(2)[C_{12}]$
119.3.o.a	$119$	$3$	119.o	17.e	$16$	$144$	$18$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.o.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
119.3.r.a	$119$	$3$	119.r	119.r	$24$	$176$	$22$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.r.a	$4$	$0$	$-4$	$-12$	$-24$	$-8$			$\mathrm{SU}(2)[C_{24}]$
119.3.t.a	$119$	$3$	119.t	119.t	$48$	$352$	$22$	$3.243$		$_{}$	None	None		✓	✓	✓	119.3.t.a	$4$	$0$	$-8$	$-8$	$-8$	$-16$			$\mathrm{SU}(2)[C_{48}]$
119.4.a.a	$119$	$4$	119.a	1.a	$1$	$1$	$1$	$7.021$	$\Q$	$_{}$	None	None	✓	✓			119.4.a.a	$1$	$0$	$-1$	$-6$	$-20$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-6q^{3}-7q^{4}-20q^{5}+6q^{6}+\cdots$
119.4.a.b	$119$	$4$	119.a	1.a	$1$	$3$	$3$	$7.021$	3.3.2429.1	$_{}$	None	None	✓	✓	✓	✓	119.4.a.b	$1$	$1$	$-1$	$5$	$-19$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
119.4.a.c	$119$	$4$	119.a	1.a	$1$	$4$	$4$	$7.021$	4.4.68557.1	$_{}$	None	None	✓	✓	✓	✓	119.4.a.c	$1$	$1$	$-2$	$-7$	$-9$	$28$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(-2-\beta _{1}-\beta _{3})q^{3}+\cdots$
119.4.a.d	$119$	$4$	119.a	1.a	$1$	$7$	$7$	$7.021$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		119.4.a.d	$1$	$0$	$4$	$5$	$35$	$-49$	$+$	$3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(7+\cdots)q^{4}+\cdots$
119.4.a.e	$119$	$4$	119.a	1.a	$1$	$9$	$9$	$7.021$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	119.4.a.e	$1$	$0$	$2$	$11$	$-3$	$63$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots$
119.4.b.a	$119$	$4$	119.b	17.b	$2$	$26$	$26$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.b.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
119.4.e.a	$119$	$4$	119.e	7.c	$3$	$28$	$14$	$7.021$		$_{}$	None	None		✓			119.4.e.a	$2$	$0$	$5$	$6$	$10$	$-38$			$\mathrm{SU}(2)[C_{3}]$
119.4.e.b	$119$	$4$	119.e	7.c	$3$	$36$	$18$	$7.021$		$_{}$	None	None		✓	✓		119.4.e.b	$2$	$0$	$-3$	$6$	$10$	$-18$			$\mathrm{SU}(2)[C_{3}]$
119.4.g.a	$119$	$4$	119.g	17.c	$4$	$52$	$26$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.g.a	$2$	$0$	$0$	$-4$	$-16$	$0$			$\mathrm{SU}(2)[C_{4}]$
119.4.j.a	$119$	$4$	119.j	119.j	$6$	$68$	$34$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.j.a	$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
119.4.k.a	$119$	$4$	119.k	17.d	$8$	$112$	$28$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.k.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
119.4.n.a	$119$	$4$	119.n	119.n	$12$	$136$	$34$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.n.a	$4$	$0$	$0$	$-2$	$6$	$-8$			$\mathrm{SU}(2)[C_{12}]$
119.4.p.a	$119$	$4$	119.p	119.p	$16$	$272$	$34$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.p.a	$4$	$0$	$-16$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{16}]$
119.4.q.a	$119$	$4$	119.q	119.q	$24$	$272$	$34$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.q.a	$4$	$0$	$-4$	$-4$	$-20$	$-8$			$\mathrm{SU}(2)[C_{24}]$
119.4.s.a	$119$	$4$	119.s	119.s	$48$	$544$	$34$	$7.021$		$_{}$	None	None		✓	✓	✓	119.4.s.a	$4$	$0$	$-8$	$-24$	$-24$	$-16$			$\mathrm{SU}(2)[C_{48}]$
119.5.c.a	$119$	$5$	119.c	7.b	$2$	$44$	$44$	$12.301$		$_{}$	None	None		✓	✓	✓	119.5.c.a	$2$	$0$	$-6$	$0$	$0$	$-130$			$\mathrm{SU}(2)[C_{2}]$
119.5.d.a	$119$	$5$	119.d	119.d	$2$	$5$	$5$	$12.301$	5.5.44253125.1	$_{}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.5.d.a	$2$	$0$	$0$	$0$	$0$	$245$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}+\beta _{4})q^{2}+(-6\beta _{1}-\beta _{4})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$
119.5.d.b	$119$	$5$	119.d	119.d	$2$	$5$	$5$	$12.301$	5.5.44253125.1	$_{}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.5.d.a	$2$	$0$	$0$	$0$	$0$	$-245$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}+\beta _{4})q^{2}+(6\beta _{1}+\beta _{4})q^{3}+(2^{4}+\cdots)q^{4}+\cdots$
119.5.d.c	$119$	$5$	119.d	119.d	$2$	$36$	$36$	$12.301$		$_{}$	None	None		✓	✓		119.5.d.c	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
119.5.f.a	$119$	$5$	119.f	119.f	$4$	$92$	$46$	$12.301$		$_{}$	None	None		✓	✓	✓	119.5.f.a	$4$	$0$	$0$	$0$	$0$	$28$			$\mathrm{SU}(2)[C_{4}]$
119.5.h.a	$119$	$5$	119.h	119.h	$6$	$92$	$46$	$12.301$		$_{}$	None	None		✓	✓	✓	119.5.h.a	$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
119.5.i.a	$119$	$5$	119.i	7.d	$6$	$84$	$42$	$12.301$		$_{}$	None	None		✓	✓	✓	119.5.i.a	$2$	$0$	$6$	$-18$	$0$	$26$			$\mathrm{SU}(2)[C_{6}]$
119.5.l.a	$119$	$5$	119.l	119.l	$8$	$184$	$46$	$12.301$		$_{}$	None	None		✓	✓	✓	119.5.l.a	$4$	$0$	$-8$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$

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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.