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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 (40 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
1975.1.c.a	$1975$	$1$	1975.c	395.c	$2$	$4$	$4$	$0.986$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-79}) $	None			✓	✓	79.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{8}-q^{9}+\beta _{2}q^{11}+\cdots$
1975.1.d.a	$1975$	$1$	1975.d	79.b	$2$	$1$	$1$	$0.986$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-395}) $	$\Q(\sqrt{5}) $	✓				395.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{9}-2q^{11}+q^{16}+2q^{19}+\cdots$
1975.1.d.b	$1975$	$1$	1975.d	79.b	$2$	$2$	$2$	$0.986$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-395}) $	None					395.1.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}-q^{4}-\beta q^{7}-q^{9}+\beta q^{12}+\cdots$
1975.1.d.c	$1975$	$1$	1975.d	79.b	$2$	$2$	$2$	$0.986$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓				79.1.b.a	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+q^{8}+q^{9}+\cdots$
1975.1.d.d	$1975$	$1$	1975.d	79.b	$2$	$4$	$4$	$0.986$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-79}) $	None	✓		✓		395.1.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{8}+\cdots$
1975.1.l.a	$1975$	$1$	1975.l	1975.l	$10$	$20$	$5$	$0.986$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		✓	✓	✓	1975.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
1975.1.m.a	$1975$	$1$	1975.m	1975.m	$10$	$20$	$5$	$0.986$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-79}) $	None		✓	✓	✓	1975.1.m.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{50}^{18}+\zeta_{50}^{22})q^{2}+(-\zeta_{50}^{11}+\cdots)q^{4}+\cdots$
1975.2.a.a	$1975$	$2$	1975.a	1.a	$1$	$1$	$1$	$15.770$	$\Q$	$_{}$	None	None	✓				395.2.b.a	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{7}-2q^{9}+q^{11}+2q^{12}+\cdots$
1975.2.a.b	$1975$	$2$	1975.a	1.a	$1$	$1$	$1$	$15.770$	$\Q$	$_{}$	None	None	✓				395.2.b.a	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{7}-2q^{9}+q^{11}-2q^{12}+\cdots$
1975.2.a.c	$1975$	$2$	1975.a	1.a	$1$	$1$	$1$	$15.770$	$\Q$	$_{}$	None	None	✓				395.2.a.c	$1$	$1$	$1$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-2q^{6}-2q^{7}-3q^{8}+\cdots$
1975.2.a.d	$1975$	$2$	1975.a	1.a	$1$	$1$	$1$	$15.770$	$\Q$	$_{}$	None	None	✓				395.2.a.b	$1$	$1$	$1$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{7}-3q^{8}-3q^{9}+4q^{11}+\cdots$
1975.2.a.e	$1975$	$2$	1975.a	1.a	$1$	$1$	$1$	$15.770$	$\Q$	$_{}$	None	None	✓				79.2.a.a	$1$	$1$	$1$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+q^{7}-3q^{8}+\cdots$
1975.2.a.f	$1975$	$2$	1975.a	1.a	$1$	$1$	$1$	$15.770$	$\Q$	$_{}$	None	None	✓				395.2.a.a	$1$	$1$	$2$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}-3q^{7}+\cdots$
1975.2.a.g	$1975$	$2$	1975.a	1.a	$1$	$3$	$3$	$15.770$	3.3.564.1	$_{}$	None	None	✓				395.2.a.f	$1$	$1$	$-6$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+2q^{4}+2\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
1975.2.a.h	$1975$	$2$	1975.a	1.a	$1$	$3$	$3$	$15.770$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				395.2.a.e	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
1975.2.a.i	$1975$	$2$	1975.a	1.a	$1$	$3$	$3$	$15.770$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓				395.2.a.d	$1$	$0$	$2$	$2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
1975.2.a.j	$1975$	$2$	1975.a	1.a	$1$	$4$	$4$	$15.770$	4.4.10273.1	$_{}$	None	None	✓				395.2.a.g	$1$	$1$	$-1$	$-2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+(3-2\beta _{1}+\cdots)q^{4}+\cdots$
1975.2.a.k	$1975$	$2$	1975.a	1.a	$1$	$5$	$5$	$15.770$	5.5.81589.1	$_{}$	None	None	✓				79.2.a.b	$1$	$0$	$0$	$-1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
1975.2.a.l	$1975$	$2$	1975.a	1.a	$1$	$6$	$6$	$15.770$	6.6.7978176.1	$_{}$	None	None	✓	✓			1975.2.a.l	$1$	$1$	$0$	$-6$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
1975.2.a.m	$1975$	$2$	1975.a	1.a	$1$	$6$	$6$	$15.770$	6.6.7978176.1	$_{}$	None	None	✓	✓			1975.2.a.l	$1$	$0$	$0$	$6$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(\beta _{2}+\beta _{4})q^{4}+\cdots$
1975.2.a.n	$1975$	$2$	1975.a	1.a	$1$	$7$	$7$	$15.770$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		1975.2.a.n	$1$	$1$	$-3$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(\beta _{3}-\beta _{5})q^{3}+(2+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
1975.2.a.o	$1975$	$2$	1975.a	1.a	$1$	$7$	$7$	$15.770$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			1975.2.a.n	$1$	$0$	$3$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-\beta _{3}+\beta _{5})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots$
1975.2.a.p	$1975$	$2$	1975.a	1.a	$1$	$11$	$11$	$15.770$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓				395.2.a.h	$1$	$0$	$0$	$2$	$0$	$-7$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(\beta _{3}+\cdots)q^{6}+\cdots$
1975.2.a.q	$1975$	$2$	1975.a	1.a	$1$	$12$	$12$	$15.770$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓				395.2.b.b	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{10}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
1975.2.a.r	$1975$	$2$	1975.a	1.a	$1$	$13$	$13$	$15.770$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓		1975.2.a.r	$1$	$1$	$-5$	$-5$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
1975.2.a.s	$1975$	$2$	1975.a	1.a	$1$	$13$	$13$	$15.770$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓		1975.2.a.r	$1$	$0$	$5$	$5$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
1975.2.a.t	$1975$	$2$	1975.a	1.a	$1$	$24$	$24$	$15.770$		$_{}$	None	None	✓		✓		395.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$
1975.4.a.a	$1975$	$4$	1975.a	1.a	$1$	$2$	$2$	$116.529$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				79.4.a.a	$1$	$1$	$1$	$2$	$0$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-4+\beta )q^{4}+\beta q^{6}+\cdots$
1975.4.a.b	$1975$	$4$	1975.a	1.a	$1$	$5$	$5$	$116.529$	5.5.4787257.1	$_{}$	None	None	✓				79.4.a.b	$1$	$1$	$3$	$8$	$0$	$20$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1+\beta _{4})q^{2}+(1+\beta _{2}-\beta _{4})q^{3}+(5+\cdots)q^{4}+\cdots$
1975.4.a.c	$1975$	$4$	1975.a	1.a	$1$	$12$	$12$	$116.529$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓				79.4.a.c	$1$	$0$	$-4$	$-8$	$0$	$-16$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{9})q^{3}+(5+\beta _{2})q^{4}+\cdots$
1975.4.a.d	$1975$	$4$	1975.a	1.a	$1$	$15$	$15$	$116.529$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓				395.4.a.a	$1$	$1$	$0$	$-2$	$0$	$24$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
1975.4.a.e	$1975$	$4$	1975.a	1.a	$1$	$16$	$16$	$116.529$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓				395.4.a.b	$1$	$0$	$6$	$16$	$0$	$74$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{7})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1975.4.a.f	$1975$	$4$	1975.a	1.a	$1$	$23$	$23$	$116.529$		$_{}$	None	None	✓				395.4.a.c	$1$	$0$	$0$	$4$	$0$	$-46$	$+$		$\mathrm{SU}(2)$
1975.4.a.g	$1975$	$4$	1975.a	1.a	$1$	$24$	$24$	$116.529$		$_{}$	None	None	✓				395.4.a.d	$1$	$1$	$-10$	$-14$	$0$	$-52$	$-$		$\mathrm{SU}(2)$
1975.4.a.h	$1975$	$4$	1975.a	1.a	$1$	$39$	$39$	$116.529$		$_{}$	None	None	✓	✓	✓		1975.4.a.h	$1$	$1$	$-10$	$-19$	$0$	$-28$	$-$		$\mathrm{SU}(2)$
1975.4.a.i	$1975$	$4$	1975.a	1.a	$1$	$39$	$39$	$116.529$		$_{}$	None	None	✓	✓			1975.4.a.i	$1$	$1$	$-6$	$-17$	$0$	$-28$	$-$		$\mathrm{SU}(2)$
1975.4.a.j	$1975$	$4$	1975.a	1.a	$1$	$39$	$39$	$116.529$		$_{}$	None	None	✓	✓	✓		1975.4.a.i	$1$	$0$	$6$	$17$	$0$	$28$	$+$		$\mathrm{SU}(2)$
1975.4.a.k	$1975$	$4$	1975.a	1.a	$1$	$39$	$39$	$116.529$		$_{}$	None	None	✓	✓			1975.4.a.h	$1$	$0$	$10$	$19$	$0$	$28$	$+$		$\mathrm{SU}(2)$
1975.4.a.l	$1975$	$4$	1975.a	1.a	$1$	$54$	$54$	$116.529$		$_{}$	None	None	✓		✓		395.4.b.a	$2$	$1$	$0$	$0$	$0$	$0$	$-$		$\mathrm{SU}(2)$
1975.4.a.m	$1975$	$4$	1975.a	1.a	$1$	$64$	$64$	$116.529$		$_{}$	None	None	✓		✓		395.4.b.b	$2$	$0$	$0$	$0$	$0$	$0$	$+$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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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.