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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 (23 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				A-L signs				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	349	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
10470.2.a.a	$10470$	$2$	10470.a	1.a	$1$	$1$	$1$	$83.603$	$\Q$	None	✓	✓			10470.2.a.a	$1$		$-1$	$-1$	$1$	$-4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
10470.2.a.b	$10470$	$2$	10470.a	1.a	$1$	$1$	$1$	$83.603$	$\Q$	None	✓	✓			10470.2.a.b	$1$		$-1$	$1$	$1$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
10470.2.a.c	$10470$	$2$	10470.a	1.a	$1$	$1$	$1$	$83.603$	$\Q$	None	✓	✓			10470.2.a.c	$1$		$1$	$-1$	$1$	$5$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+5q^{7}+\cdots$
10470.2.a.d	$10470$	$2$	10470.a	1.a	$1$	$1$	$1$	$83.603$	$\Q$	None	✓	✓			10470.2.a.d	$1$		$1$	$1$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
10470.2.a.e	$10470$	$2$	10470.a	1.a	$1$	$1$	$1$	$83.603$	$\Q$	None	✓	✓			10470.2.a.e	$1$		$1$	$1$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
10470.2.a.f	$10470$	$2$	10470.a	1.a	$1$	$2$	$2$	$83.603$	$\Q(\sqrt{2}) $	None	✓	✓			10470.2.a.f	$1$		$2$	$2$	$-2$	$-6$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
10470.2.a.g	$10470$	$2$	10470.a	1.a	$1$	$5$	$5$	$83.603$	5.5.24217.1	None	✓	✓			10470.2.a.g	$1$		$5$	$5$	$5$	$-8$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
10470.2.a.h	$10470$	$2$	10470.a	1.a	$1$	$5$	$5$	$83.603$	5.5.305617.1	None	✓	✓			10470.2.a.h	$1$		$5$	$5$	$5$	$-8$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
10470.2.a.i	$10470$	$2$	10470.a	1.a	$1$	$10$	$10$	$83.603$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.i	$1$		$10$	$10$	$-10$	$-8$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
10470.2.a.j	$10470$	$2$	10470.a	1.a	$1$	$12$	$12$	$83.603$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.j	$1$		$-12$	$12$	$-12$	$0$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
10470.2.a.k	$10470$	$2$	10470.a	1.a	$1$	$12$	$12$	$83.603$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		10470.2.a.k	$1$		$-12$	$12$	$12$	$-11$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
10470.2.a.l	$10470$	$2$	10470.a	1.a	$1$	$12$	$12$	$83.603$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.l	$1$		$12$	$-12$	$-12$	$-2$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
10470.2.a.m	$10470$	$2$	10470.a	1.a	$1$	$12$	$12$	$83.603$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.m	$1$		$12$	$-12$	$12$	$-6$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
10470.2.a.n	$10470$	$2$	10470.a	1.a	$1$	$14$	$14$	$83.603$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.n	$1$		$-14$	$-14$	$-14$	$-9$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
10470.2.a.o	$10470$	$2$	10470.a	1.a	$1$	$14$	$14$	$83.603$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓		10470.2.a.o	$1$		$-14$	$-14$	$14$	$2$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
10470.2.a.p	$10470$	$2$	10470.a	1.a	$1$	$14$	$14$	$83.603$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.p	$1$		$-14$	$-14$	$14$	$5$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
10470.2.a.q	$10470$	$2$	10470.a	1.a	$1$	$15$	$15$	$83.603$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.q	$1$		$-15$	$-15$	$-15$	$8$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
10470.2.a.r	$10470$	$2$	10470.a	1.a	$1$	$16$	$16$	$83.603$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.r	$1$		$-16$	$16$	$-16$	$9$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
10470.2.a.s	$10470$	$2$	10470.a	1.a	$1$	$16$	$16$	$83.603$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓	✓		10470.2.a.s	$1$		$16$	$-16$	$16$	$2$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
10470.2.a.t	$10470$	$2$	10470.a	1.a	$1$	$17$	$17$	$83.603$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.t	$1$		$-17$	$17$	$17$	$11$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
10470.2.a.u	$10470$	$2$	10470.a	1.a	$1$	$17$	$17$	$83.603$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	✓	✓	✓	10470.2.a.u	$1$		$17$	$-17$	$-17$	$-1$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
10470.2.a.v	$10470$	$2$	10470.a	1.a	$1$	$17$	$17$	$83.603$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	✓	✓		10470.2.a.v	$1$		$17$	$17$	$17$	$13$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
10470.2.a.w	$10470$	$2$	10470.a	1.a	$1$	$18$	$18$	$83.603$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓		10470.2.a.w	$1$		$18$	$18$	$-18$	$13$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$

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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.