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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 106 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
250.2.a.a	$250$	$2$	250.a	1.a	$1$	$2$	$2$	$1.996$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	250.2.a.a	$1$	$1$	$-2$	$-3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
250.2.a.b	$250$	$2$	250.a	1.a	$1$	$2$	$2$	$1.996$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	250.2.a.b	$1$	$0$	$-2$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}-2\beta q^{6}-\beta q^{7}+\cdots$
250.2.a.c	$250$	$2$	250.a	1.a	$1$	$2$	$2$	$1.996$	$\Q(\sqrt{5}) $	None	✓	✓			250.2.a.b	$1$	$0$	$2$	$-2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2\beta q^{3}+q^{4}-2\beta q^{6}+\beta q^{7}+\cdots$
250.2.a.d	$250$	$2$	250.a	1.a	$1$	$2$	$2$	$1.996$	$\Q(\sqrt{5}) $	None	✓	✓			250.2.a.a	$1$	$0$	$2$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
250.2.b.a	$250$	$2$	250.b	5.b	$2$	$4$	$4$	$1.996$	$\Q(i, \sqrt{5})$	None		✓			250.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+2\beta _{1}q^{3}-q^{4}+2\beta _{2}q^{6}+\cdots$
250.2.b.b	$250$	$2$	250.b	5.b	$2$	$4$	$4$	$1.996$	$\Q(i, \sqrt{5})$	None		✓			250.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots$
250.2.d.a	$250$	$2$	250.d	25.d	$5$	$4$	$1$	$1.996$	$\Q(\zeta_{10})$	None					50.2.d.a	$2$	$0$	$-1$	$1$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
250.2.d.b	$250$	$2$	250.d	25.d	$5$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	None					50.2.e.a	$2$	$0$	$-2$	$2$	$0$	$-16$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{20}q^{2}+(-\zeta_{20}^{3}+\zeta_{20}^{5})q^{3}+\zeta_{20}^{3}q^{4}+\cdots$
250.2.d.c	$250$	$2$	250.d	25.d	$5$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	None					50.2.e.a	$2$	$0$	$2$	$-2$	$0$	$16$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{20}^{4}q^{2}+(-\zeta_{20}+\zeta_{20}^{2})q^{3}-\zeta_{20}q^{4}+\cdots$
250.2.d.d	$250$	$2$	250.d	25.d	$5$	$8$	$2$	$1.996$	8.0.58140625.2	None					50.2.d.b	$2$	$0$	$2$	$3$	$0$	$-4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}-\beta _{3}-\beta _{6})q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\cdots$
250.2.e.a	$250$	$2$	250.e	25.e	$10$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	None					50.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+(1-\zeta_{20}^{2}+\zeta_{20}^{4}-2\zeta_{20}^{6}+\cdots)q^{3}+\cdots$
250.2.e.b	$250$	$2$	250.e	25.e	$10$	$8$	$2$	$1.996$	$\Q(\zeta_{20})$	None					50.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+(\zeta_{20}-\zeta_{20}^{3}+\zeta_{20}^{7})q^{3}+\cdots$
250.2.e.c	$250$	$2$	250.e	25.e	$10$	$16$	$4$	$1.996$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None			✓		50.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{9}+\beta _{10}+\beta _{12}-\beta _{13})q^{2}+(-\beta _{9}+\cdots)q^{3}+\cdots$
250.2.g.a	$250$	$2$	250.g	125.g	$25$	$120$	$6$	$1.996$		None		✓			250.2.g.a	$2$	$0$	$0$	$0$	$-5$	$10$			$\mathrm{SU}(2)[C_{25}]$
250.2.g.b	$250$	$2$	250.g	125.g	$25$	$140$	$7$	$1.996$		None		✓	✓		250.2.g.b	$2$	$0$	$0$	$0$	$-5$	$-10$			$\mathrm{SU}(2)[C_{25}]$
250.2.h.a	$250$	$2$	250.h	125.h	$50$	$240$	$12$	$1.996$		None		✓	✓	✓	250.2.h.a	$2$	$0$	$0$	$0$	$10$	$0$			$\mathrm{SU}(2)[C_{50}]$
250.3.c.a	$250$	$3$	250.c	5.c	$4$	$8$	$4$	$6.812$	$\Q(\zeta_{20})$	None		✓			250.3.c.a	$2$	$0$	$-8$	$-6$	$0$	$26$		$2^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{20})q^{2}+(-1+\zeta_{20}-\zeta_{20}^{3}+\cdots)q^{3}+\cdots$
250.3.c.b	$250$	$3$	250.c	5.c	$4$	$8$	$4$	$6.812$	8.0.1024000000.2	None		✓			250.3.c.b	$2$	$0$	$-8$	$4$	$0$	$-24$		$5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$
250.3.c.c	$250$	$3$	250.c	5.c	$4$	$8$	$4$	$6.812$	8.0.1024000000.2	None		✓			250.3.c.b	$2$	$0$	$8$	$-4$	$0$	$24$		$5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{4}+\cdots$
250.3.c.d	$250$	$3$	250.c	5.c	$4$	$8$	$4$	$6.812$	$\Q(\zeta_{20})$	None		✓			250.3.c.a	$2$	$0$	$8$	$6$	$0$	$-26$		$2^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{20})q^{2}+(1+\zeta_{20}+\zeta_{20}^{3})q^{3}+\cdots$
250.3.f.a	$250$	$3$	250.f	25.f	$20$	$16$	$2$	$6.812$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					50.3.f.a	$2$	$0$	$-4$	$2$	$0$	$-2$		$5^{2}$	$\mathrm{SU}(2)[C_{20}]$	$q+(-1-\beta _{2}+\beta _{7}-\beta _{8}-\beta _{9})q^{2}+(1+\cdots)q^{3}+\cdots$
250.3.f.b	$250$	$3$	250.f	25.f	$20$	$16$	$2$	$6.812$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					50.3.f.a	$2$	$0$	$4$	$-2$	$0$	$2$		$5^{2}$	$\mathrm{SU}(2)[C_{20}]$	$q+(-\beta _{1}-\beta _{9})q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{7}+\cdots)q^{3}+\cdots$
250.3.f.c	$250$	$3$	250.f	25.f	$20$	$16$	$2$	$6.812$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					50.3.f.a	$2$	$0$	$4$	$-2$	$0$	$2$		$5^{2}$	$\mathrm{SU}(2)[C_{20}]$	$q+(\beta _{1}-\beta _{9})q^{2}+(-\beta _{4}+\beta _{11})q^{3}-2\beta _{3}q^{4}+\cdots$
250.3.f.d	$250$	$3$	250.f	25.f	$20$	$24$	$3$	$6.812$		None					50.3.f.b	$2$	$0$	$-6$	$-2$	$0$	$2$			$\mathrm{SU}(2)[C_{20}]$
250.3.f.e	$250$	$3$	250.f	25.f	$20$	$24$	$3$	$6.812$		None					50.3.f.b	$2$	$0$	$-6$	$-2$	$0$	$2$			$\mathrm{SU}(2)[C_{20}]$
250.3.f.f	$250$	$3$	250.f	25.f	$20$	$24$	$3$	$6.812$		None					50.3.f.b	$2$	$0$	$6$	$2$	$0$	$-2$			$\mathrm{SU}(2)[C_{20}]$
250.3.i.a	$250$	$3$	250.i	125.i	$100$	$480$	$12$	$6.812$		None		✓			250.3.i.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{100}]$
250.3.i.b	$250$	$3$	250.i	125.i	$100$	$520$	$13$	$6.812$		None		✓	✓		250.3.i.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{100}]$
250.4.a.a	$250$	$4$	250.a	1.a	$1$	$2$	$2$	$14.750$	$\Q(\sqrt{5}) $	None	✓	✓			250.4.a.a	$1$	$1$	$-4$	$1$	$0$	$28$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}+(15+\cdots)q^{7}+\cdots$
250.4.a.b	$250$	$4$	250.a	1.a	$1$	$2$	$2$	$14.750$	$\Q(\sqrt{5}) $	None	✓	✓			250.4.a.b	$1$	$0$	$-4$	$11$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(4+3\beta )q^{3}+4q^{4}+(-8-6\beta )q^{6}+\cdots$
250.4.a.c	$250$	$4$	250.a	1.a	$1$	$2$	$2$	$14.750$	$\Q(\sqrt{5}) $	None	✓	✓			250.4.a.b	$1$	$1$	$4$	$-11$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-4-3\beta )q^{3}+4q^{4}+(-8+\cdots)q^{6}+\cdots$
250.4.a.d	$250$	$4$	250.a	1.a	$1$	$2$	$2$	$14.750$	$\Q(\sqrt{5}) $	None	✓	✓			250.4.a.a	$1$	$1$	$4$	$-1$	$0$	$-28$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta q^{3}+4q^{4}-2\beta q^{6}+(-15+\cdots)q^{7}+\cdots$
250.4.a.e	$250$	$4$	250.a	1.a	$1$	$4$	$4$	$14.750$	4.4.22000.1	None	✓	✓	✓		250.4.a.e	$1$	$1$	$-8$	$-8$	$0$	$-34$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2-\beta _{2})q^{3}+4q^{4}+(4+2\beta _{2}+\cdots)q^{6}+\cdots$
250.4.a.f	$250$	$4$	250.a	1.a	$1$	$4$	$4$	$14.750$	4.4.18625.1	None	✓	✓	✓		250.4.a.f	$1$	$0$	$-8$	$-3$	$0$	$-9$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1-\beta _{3})q^{3}+4q^{4}+(2+2\beta _{3})q^{6}+\cdots$
250.4.a.g	$250$	$4$	250.a	1.a	$1$	$4$	$4$	$14.750$	4.4.18625.1	None	✓	✓			250.4.a.f	$1$	$0$	$8$	$3$	$0$	$9$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{3})q^{3}+4q^{4}+(2+2\beta _{3})q^{6}+\cdots$
250.4.a.h	$250$	$4$	250.a	1.a	$1$	$4$	$4$	$14.750$	4.4.22000.1	None	✓	✓			250.4.a.e	$1$	$0$	$8$	$8$	$0$	$34$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+(2-\beta _{2})q^{3}+4q^{4}+(4-2\beta _{2}+\cdots)q^{6}+\cdots$
250.4.b.a	$250$	$4$	250.b	5.b	$2$	$4$	$4$	$14.750$	$\Q(i, \sqrt{5})$	None		✓			250.4.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{3}q^{2}+(-3\beta _{1}+4\beta _{3})q^{3}-4q^{4}+\cdots$
250.4.b.b	$250$	$4$	250.b	5.b	$2$	$4$	$4$	$14.750$	$\Q(i, \sqrt{5})$	None		✓			250.4.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{3}q^{2}+\beta _{1}q^{3}-4q^{4}+2\beta _{2}q^{6}+\cdots$
250.4.b.c	$250$	$4$	250.b	5.b	$2$	$8$	$8$	$14.750$	8.0.$\cdots$.2	None		✓			250.4.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{4}q^{2}+(\beta _{4}+\beta _{7})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots$
250.4.b.d	$250$	$4$	250.b	5.b	$2$	$8$	$8$	$14.750$	8.0.$\cdots$.21	None		✓			250.4.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-4q^{4}+(5+\beta _{3}+\cdots)q^{6}+\cdots$
250.4.d.a	$250$	$4$	250.d	25.d	$5$	$12$	$3$	$14.750$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					50.4.d.a	$2$	$0$	$-6$	$-1$	$0$	$-58$		$5^{3}$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{5}q^{2}+(\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$
250.4.d.b	$250$	$4$	250.d	25.d	$5$	$16$	$4$	$14.750$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					50.4.d.b	$2$	$0$	$8$	$-7$	$0$	$54$		$5^{6}$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{8}q^{2}+(-1+\beta _{4}+\beta _{7})q^{3}+(-4+\cdots)q^{4}+\cdots$
250.4.d.c	$250$	$4$	250.d	25.d	$5$	$32$	$8$	$14.750$		None					50.4.e.a	$2$	$0$	$-16$	$-6$	$0$	$112$			$\mathrm{SU}(2)[C_{5}]$
250.4.d.d	$250$	$4$	250.d	25.d	$5$	$32$	$8$	$14.750$		None					50.4.e.a	$2$	$0$	$16$	$6$	$0$	$-112$			$\mathrm{SU}(2)[C_{5}]$
250.4.e.a	$250$	$4$	250.e	25.e	$10$	$24$	$6$	$14.750$		None					50.4.d.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
250.4.e.b	$250$	$4$	250.e	25.e	$10$	$32$	$8$	$14.750$		None					50.4.e.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
250.4.e.c	$250$	$4$	250.e	25.e	$10$	$32$	$8$	$14.750$		None					50.4.d.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
250.4.g.a	$250$	$4$	250.g	125.g	$25$	$360$	$18$	$14.750$		None		✓			250.4.g.a	$2$	$0$	$0$	$0$	$-20$	$-70$			$\mathrm{SU}(2)[C_{25}]$
250.4.g.b	$250$	$4$	250.g	125.g	$25$	$380$	$19$	$14.750$		None		✓	✓		250.4.g.b	$2$	$0$	$0$	$0$	$-20$	$70$			$\mathrm{SU}(2)[C_{25}]$
250.4.h.a	$250$	$4$	250.h	125.h	$50$	$760$	$38$	$14.750$		None		✓	✓	✓	250.4.h.a	$2$	$0$	$0$	$0$	$40$	$0$			$\mathrm{SU}(2)[C_{50}]$

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Elliptic curves over $\Q$
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Genus 2 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.