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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 66 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
625.2.a.a	$625$	$2$	625.a	1.a	$1$	$2$	$2$	$4.991$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$-3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
625.2.a.b	$625$	$2$	625.a	1.a	$1$	$2$	$2$	$4.991$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
625.2.a.c	$625$	$2$	625.a	1.a	$1$	$2$	$2$	$4.991$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$1$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
625.2.a.d	$625$	$2$	625.a	1.a	$1$	$2$	$2$	$4.991$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{6}+\cdots$
625.2.a.e	$625$	$2$	625.a	1.a	$1$	$8$	$8$	$4.991$	8.8.6152203125.1	None	✓	$1$	$1$	$-5$	$-5$	$0$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(\beta _{3}-\beta _{5}+\beta _{7})q^{3}+\cdots$
625.2.a.f	$625$	$2$	625.a	1.a	$1$	$8$	$8$	$4.991$	8.8.$\cdots$.2	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
625.2.a.g	$625$	$2$	625.a	1.a	$1$	$8$	$8$	$4.991$	8.8.6152203125.1	None	✓	$1$	$0$	$5$	$5$	$0$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-\beta _{3}+\beta _{5}-\beta _{7})q^{3}+\cdots$
625.2.b.a	$625$	$2$	625.b	5.b	$2$	$4$	$4$	$4.991$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$
625.2.b.b	$625$	$2$	625.b	5.b	$2$	$4$	$4$	$4.991$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
625.2.b.c	$625$	$2$	625.b	5.b	$2$	$8$	$8$	$4.991$	8.0.58140625.2	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(\beta _{5}+\beta _{6})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
625.2.b.d	$625$	$2$	625.b	5.b	$2$	$16$	$16$	$4.991$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-\beta _{10}q^{3}+(-1-\beta _{12})q^{4}+\cdots$
625.2.d.a	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$-3$	$-4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
625.2.d.b	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$-3$	$1$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
625.2.d.c	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$-3$	$1$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}^{3})q^{2}+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+\cdots$
625.2.d.d	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$1$	$-2$	$-1$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\cdots)q^{3}+\cdots$
625.2.d.e	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$-2$	$4$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots$
625.2.d.f	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$2$	$-4$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
625.2.d.g	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$2$	$1$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+\cdots$
625.2.d.h	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$3$	$-1$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
625.2.d.i	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$3$	$-1$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{3}+\cdots$
625.2.d.j	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	$\Q(\zeta_{10})$	None		$2$	$0$	$3$	$4$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots$
625.2.d.k	$625$	$2$	625.d	25.d	$5$	$8$	$2$	$4.991$	8.0.484000000.9	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}-\beta _{6})q^{2}+(-\beta _{1}+\beta _{6}+\beta _{7})q^{3}+\cdots$
625.2.d.l	$625$	$2$	625.d	25.d	$5$	$8$	$2$	$4.991$	8.0.484000000.9	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
625.2.d.m	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-5$	$0$	$0$	$20$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6})q^{2}+(\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$
625.2.d.n	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$-5$	$0$	$20$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}-\beta _{6}+\beta _{7}-\beta _{8}-\beta _{12})q^{2}+\cdots$
625.2.d.o	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{11}-\beta _{13})q^{2}+(-\beta _{6}+\beta _{11}+\cdots)q^{3}+\cdots$
625.2.d.p	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$5$	$0$	$-20$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{5}+\beta _{6}-\beta _{7}+\beta _{8}+\beta _{12})q^{2}+(1+\cdots)q^{3}+\cdots$
625.2.d.q	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$5$	$0$	$0$	$-20$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(\beta _{5}-\beta _{15})q^{3}+\cdots$
625.2.e.a	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	8.0.58140625.2	None		$2$	$0$	$0$	$-5$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}+\beta _{5}+\beta _{7})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
625.2.e.b	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	8.0.484000000.6	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(1+\beta _{2}-3\beta _{3}+\cdots)q^{4}+\cdots$
625.2.e.c	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}q^{3}+(-1+\cdots)q^{4}+\cdots$
625.2.e.d	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(\zeta_{20}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}+\cdots$
625.2.e.e	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots$
625.2.e.f	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(\zeta_{20}+\cdots)q^{3}+\cdots$
625.2.e.g	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(2\zeta_{20}+\cdots)q^{3}+\cdots$
625.2.e.h	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	8.0.484000000.6	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{6})q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\cdots$
625.2.e.i	$625$	$2$	625.e	25.e	$10$	$8$	$2$	$4.991$	8.0.58140625.2	None		$2$	$0$	$0$	$5$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\beta _{4}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{3}+\cdots$
625.2.e.j	$625$	$2$	625.e	25.e	$10$	$32$	$8$	$4.991$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
625.2.e.k	$625$	$2$	625.e	25.e	$10$	$32$	$8$	$4.991$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
625.2.g.a	$625$	$2$	625.g	125.g	$25$	$220$	$11$	$4.991$		None		$2$	$0$	$20$	$20$	$0$	$15$			$\mathrm{SU}(2)[C_{25}]$
625.2.g.b	$625$	$2$	625.g	125.g	$25$	$480$	$24$	$4.991$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{25}]$
625.2.h.a	$625$	$2$	625.h	125.h	$50$	$240$	$12$	$4.991$		None		$2$	$0$	$20$	$20$	$0$	$25$			$\mathrm{SU}(2)[C_{50}]$
625.2.h.b	$625$	$2$	625.h	125.h	$50$	$440$	$22$	$4.991$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{50}]$
625.2.j.a	$625$	$2$	625.j	625.j	$125$	$6100$	$61$	$4.991$		None		$2$	$0$	$-100$	$-100$	$-100$	$-100$			$\mathrm{SU}(2)[C_{125}]$
625.2.k.a	$625$	$2$	625.k	625.k	$250$	$6200$	$62$	$4.991$		None		$2$	$0$	$-100$	$-100$	$-100$	$-100$			$\mathrm{SU}(2)[C_{250}]$
625.4.a.a	$625$	$4$	625.a	1.a	$1$	$10$	$10$	$36.876$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-3$	$-1$	$0$	$-38$	$-$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{9}q^{3}+(5+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
625.4.a.b	$625$	$4$	625.a	1.a	$1$	$10$	$10$	$36.876$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$3$	$1$	$0$	$38$	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(5+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
625.4.a.c	$625$	$4$	625.a	1.a	$1$	$14$	$14$	$36.876$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$-3$	$-1$	$0$	$-8$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots$
625.4.a.d	$625$	$4$	625.a	1.a	$1$	$14$	$14$	$36.876$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$3$	$1$	$0$	$8$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots$
625.4.a.e	$625$	$4$	625.a	1.a	$1$	$20$	$20$	$36.876$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$-9$	$-23$	$0$	$-64$	$-$	$5^{9}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{8})q^{3}+(3+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
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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.