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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 702638 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
10001.2.a.a	$10001$	$2$	10001.a	1.a	$1$	$1$	$1$	$79.858$	$\Q$	None	✓	✓			10001.2.a.a	$1$		$1$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{5}-4q^{7}-3q^{8}-3q^{9}+\cdots$
10001.2.a.b	$10001$	$2$	10001.a	1.a	$1$	$184$	$184$	$79.858$		None	✓	✓	✓	✓	10001.2.a.b	$1$		$-6$	$-16$	$-4$	$-28$	$+$		$\mathrm{SU}(2)$
10001.2.a.c	$10001$	$2$	10001.a	1.a	$1$	$184$	$184$	$79.858$		None	✓	✓	✓		10001.2.a.c	$1$		$-4$	$-20$	$-10$	$-52$	$+$		$\mathrm{SU}(2)$
10001.2.a.d	$10001$	$2$	10001.a	1.a	$1$	$224$	$224$	$79.858$		None	✓	✓	✓	✓	10001.2.a.d	$1$		$6$	$16$	$8$	$64$	$-$		$\mathrm{SU}(2)$
10001.2.a.e	$10001$	$2$	10001.a	1.a	$1$	$224$	$224$	$79.858$		None	✓	✓	✓	✓	10001.2.a.e	$1$		$6$	$24$	$12$	$28$	$-$		$\mathrm{SU}(2)$
10002.2.a.a	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	$\Q$	None	✓	✓			10002.2.a.a	$1$		$-1$	$-1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots$
10002.2.a.b	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	$\Q$	None	✓	✓			10002.2.a.b	$1$		$-1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots$
10002.2.a.c	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	$\Q$	None	✓	✓			10002.2.a.c	$1$		$-1$	$-1$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots$
10002.2.a.d	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	$\Q$	None	✓	✓			10002.2.a.d	$1$		$1$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
10002.2.a.e	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	$\Q$	None	✓	✓			10002.2.a.e	$1$		$1$	$1$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots$
10002.2.a.f	$10002$	$2$	10002.a	1.a	$1$	$3$	$3$	$79.866$	3.3.148.1	None	✓	✓			10002.2.a.f	$1$		$3$	$3$	$-6$	$-4$	$+$		$\mathrm{SU}(2)$
10002.2.a.g	$10002$	$2$	10002.a	1.a	$1$	$19$	$19$	$79.866$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	✓	✓		10002.2.a.g	$1$		$19$	$19$	$-5$	$-13$	$+$		$\mathrm{SU}(2)$
10002.2.a.h	$10002$	$2$	10002.a	1.a	$1$	$28$	$28$	$79.866$		None	✓	✓	✓		10002.2.a.h	$1$		$-28$	$-28$	$3$	$5$	$-$		$\mathrm{SU}(2)$
10002.2.a.i	$10002$	$2$	10002.a	1.a	$1$	$29$	$29$	$79.866$		None	✓	✓	✓		10002.2.a.i	$1$		$29$	$-29$	$-10$	$-5$	$+$		$\mathrm{SU}(2)$
10002.2.a.j	$10002$	$2$	10002.a	1.a	$1$	$32$	$32$	$79.866$		None	✓	✓	✓	✓	10002.2.a.j	$1$		$-32$	$32$	$0$	$-26$	$+$		$\mathrm{SU}(2)$
10002.2.a.k	$10002$	$2$	10002.a	1.a	$1$	$38$	$38$	$79.866$		None	✓	✓	✓		10002.2.a.k	$1$		$-38$	$-38$	$-3$	$-12$	$+$		$\mathrm{SU}(2)$
10002.2.a.l	$10002$	$2$	10002.a	1.a	$1$	$38$	$38$	$79.866$		None	✓	✓	✓	✓	10002.2.a.l	$1$		$-38$	$38$	$2$	$25$	$-$		$\mathrm{SU}(2)$
10002.2.a.m	$10002$	$2$	10002.a	1.a	$1$	$40$	$40$	$79.866$		None	✓	✓	✓	✓	10002.2.a.m	$1$		$40$	$-40$	$14$	$8$	$-$		$\mathrm{SU}(2)$
10002.2.a.n	$10002$	$2$	10002.a	1.a	$1$	$47$	$47$	$79.866$		None	✓	✓	✓	✓	10002.2.a.n	$1$		$47$	$47$	$11$	$24$	$-$		$\mathrm{SU}(2)$
10003.2.a.a	$10003$	$2$	10003.a	1.a	$1$	$1$	$1$	$79.874$	$\Q$	None	✓	✓			10003.2.a.a	$1$		$-1$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}-2q^{6}-q^{7}+3q^{8}+\cdots$
10003.2.a.b	$10003$	$2$	10003.a	1.a	$1$	$168$	$168$	$79.874$		None	✓	✓	✓	✓	10003.2.a.b	$1$		$-36$	$-16$	$-49$	$168$	$+$		$\mathrm{SU}(2)$
10003.2.a.c	$10003$	$2$	10003.a	1.a	$1$	$178$	$178$	$79.874$		None	✓	✓	✓	✓	10003.2.a.c	$1$		$-18$	$-20$	$-55$	$-178$	$+$		$\mathrm{SU}(2)$
10003.2.a.d	$10003$	$2$	10003.a	1.a	$1$	$178$	$178$	$79.874$		None	✓	✓	✓		10003.2.a.d	$1$		$20$	$14$	$53$	$-178$	$-$		$\mathrm{SU}(2)$
10003.2.a.e	$10003$	$2$	10003.a	1.a	$1$	$190$	$190$	$79.874$		None	✓	✓	✓	✓	10003.2.a.e	$1$		$36$	$16$	$53$	$190$	$-$		$\mathrm{SU}(2)$
10004.2.a.a	$10004$	$2$	10004.a	1.a	$1$	$1$	$1$	$79.882$	$\Q$	None	✓	✓			10004.2.a.a	$1$		$0$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-3q^{9}-q^{11}-2q^{13}+7q^{17}+\cdots$
10004.2.a.b	$10004$	$2$	10004.a	1.a	$1$	$42$	$42$	$79.882$		None	✓	✓	✓		10004.2.a.b	$1$		$0$	$-1$	$-12$	$-8$	$+$		$\mathrm{SU}(2)$
10004.2.a.c	$10004$	$2$	10004.a	1.a	$1$	$43$	$43$	$79.882$		None	✓	✓	✓	✓	10004.2.a.c	$1$		$0$	$-1$	$-9$	$-10$	$+$		$\mathrm{SU}(2)$
10004.2.a.d	$10004$	$2$	10004.a	1.a	$1$	$57$	$57$	$79.882$		None	✓	✓	✓	✓	10004.2.a.d	$1$		$0$	$-1$	$7$	$12$	$-$		$\mathrm{SU}(2)$
10004.2.a.e	$10004$	$2$	10004.a	1.a	$1$	$57$	$57$	$79.882$		None	✓	✓	✓	✓	10004.2.a.e	$1$		$0$	$-1$	$7$	$14$	$-$		$\mathrm{SU}(2)$
10005.2.a.a	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.a	$1$		$-2$	$1$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+3q^{7}+\cdots$
10005.2.a.b	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.b	$1$		$-1$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
10005.2.a.c	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.c	$1$		$-1$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
10005.2.a.d	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.d	$1$		$-1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$
10005.2.a.e	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.e	$1$		$0$	$-1$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}-5q^{7}+q^{9}+2q^{12}+\cdots$
10005.2.a.f	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.f	$1$		$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+4q^{11}+\cdots$
10005.2.a.g	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.g	$1$		$0$	$1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-4q^{11}+\cdots$
10005.2.a.h	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.h	$1$		$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-2q^{12}+\cdots$
10005.2.a.i	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.i	$1$		$0$	$1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
10005.2.a.j	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.j	$1$		$0$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{7}+q^{9}-2q^{12}+\cdots$
10005.2.a.k	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.k	$1$		$1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots$
10005.2.a.l	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.l	$1$		$1$	$-1$	$1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
10005.2.a.m	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.m	$1$		$1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots$
10005.2.a.n	$10005$	$2$	10005.a	1.a	$1$	$1$	$1$	$79.890$	$\Q$	None	✓	✓			10005.2.a.n	$1$		$2$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{7}+\cdots$
10005.2.a.o	$10005$	$2$	10005.a	1.a	$1$	$2$	$2$	$79.890$	$\Q(\sqrt{57}) $	None	✓	✓			10005.2.a.o	$1$		$0$	$2$	$2$	$1$	$-$		$\mathrm{SU}(2)$
10005.2.a.p	$10005$	$2$	10005.a	1.a	$1$	$2$	$2$	$79.890$	$\Q(\sqrt{2}) $	None	✓	✓			10005.2.a.p	$1$		$0$	$2$	$2$	$2$	$+$		$\mathrm{SU}(2)$
10005.2.a.q	$10005$	$2$	10005.a	1.a	$1$	$2$	$2$	$79.890$	$\Q(\sqrt{17}) $	None	✓	✓			10005.2.a.q	$1$		$1$	$2$	$2$	$-1$	$-$		$\mathrm{SU}(2)$
10005.2.a.r	$10005$	$2$	10005.a	1.a	$1$	$2$	$2$	$79.890$	$\Q(\sqrt{2}) $	None	✓	✓			10005.2.a.r	$1$		$2$	$-2$	$-2$	$0$	$+$		$\mathrm{SU}(2)$
10005.2.a.s	$10005$	$2$	10005.a	1.a	$1$	$18$	$18$	$79.890$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓		10005.2.a.s	$1$		$-5$	$18$	$18$	$-24$	$+$		$\mathrm{SU}(2)$
10005.2.a.t	$10005$	$2$	10005.a	1.a	$1$	$19$	$19$	$79.890$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	✓	✓		10005.2.a.t	$1$		$-3$	$-19$	$-19$	$-2$	$+$		$\mathrm{SU}(2)$
10005.2.a.u	$10005$	$2$	10005.a	1.a	$1$	$20$	$20$	$79.890$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	✓	✓		10005.2.a.u	$1$		$-3$	$20$	$-20$	$0$	$+$		$\mathrm{SU}(2)$

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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.