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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 67 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
783.1.d.a	$783$	$1$	783.d	87.d	$2$	$3$	$3$	$0.391$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	✓			783.1.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(-1+\cdots)q^{8}+\cdots$
783.1.d.b	$783$	$1$	783.d	87.d	$2$	$3$	$3$	$0.391$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	✓			783.1.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots$
783.2.a.a	$783$	$2$	783.a	1.a	$1$	$2$	$2$	$6.252$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			783.2.a.a	$1$	$1$	$-1$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1-\beta )q^{7}+\cdots$
783.2.a.b	$783$	$2$	783.a	1.a	$1$	$2$	$2$	$6.252$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			783.2.a.b	$1$	$1$	$-1$	$0$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}-2q^{5}+(-1-\beta )q^{7}+\cdots$
783.2.a.c	$783$	$2$	783.a	1.a	$1$	$2$	$2$	$6.252$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			783.2.a.a	$1$	$1$	$1$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots$
783.2.a.d	$783$	$2$	783.a	1.a	$1$	$2$	$2$	$6.252$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			783.2.a.b	$1$	$0$	$1$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+2q^{5}+(-1-\beta )q^{7}+\cdots$
783.2.a.e	$783$	$2$	783.a	1.a	$1$	$3$	$3$	$6.252$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓	✓		783.2.a.e	$1$	$1$	$-2$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
783.2.a.f	$783$	$2$	783.a	1.a	$1$	$3$	$3$	$6.252$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓			783.2.a.e	$1$	$0$	$2$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
783.2.a.g	$783$	$2$	783.a	1.a	$1$	$4$	$4$	$6.252$	4.4.15529.1	$_{}$	None	None	✓	✓	✓		783.2.a.g	$1$	$1$	$-3$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
783.2.a.h	$783$	$2$	783.a	1.a	$1$	$4$	$4$	$6.252$	4.4.15529.1	$_{}$	None	None	✓	✓			783.2.a.g	$1$	$0$	$3$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
783.2.a.i	$783$	$2$	783.a	1.a	$1$	$8$	$8$	$6.252$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		783.2.a.i	$1$	$0$	$-1$	$0$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
783.2.a.j	$783$	$2$	783.a	1.a	$1$	$8$	$8$	$6.252$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		783.2.a.i	$1$	$0$	$1$	$0$	$-2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
783.2.c.a	$783$	$2$	783.c	29.b	$2$	$8$	$8$	$6.252$	8.0.$\cdots$.2	$_{}$	None	None		✓			783.2.c.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{1}q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots$
783.2.c.b	$783$	$2$	783.c	29.b	$2$	$12$	$12$	$6.252$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-87}) $	None		✓			783.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$3^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{8}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots$
783.2.c.c	$783$	$2$	783.c	29.b	$2$	$20$	$20$	$6.252$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		783.2.c.c	$4$	$0$	$0$	$0$	$0$	$8$		$2^{5}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{12}q^{2}+(-1+\beta _{10})q^{4}+\beta _{1}q^{5}+\cdots$
783.2.e.a	$783$	$2$	783.e	9.c	$3$	$22$	$11$	$6.252$		$_{}$	None	None					261.2.e.a	$2$	$0$	$1$	$0$	$-1$	$7$			$\mathrm{SU}(2)[C_{3}]$
783.2.e.b	$783$	$2$	783.e	9.c	$3$	$34$	$17$	$6.252$		$_{}$	None	None			✓		261.2.e.b	$2$	$0$	$1$	$0$	$-1$	$-9$			$\mathrm{SU}(2)[C_{3}]$
783.2.g.a	$783$	$2$	783.g	87.f	$4$	$8$	$4$	$6.252$	8.0.$\cdots$.8	$_{}$	None	None		✓			783.2.g.a	$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2\beta _{2}q^{4}+\beta _{1}q^{5}+(-1+\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots$
783.2.g.b	$783$	$2$	783.g	87.f	$4$	$32$	$16$	$6.252$		$_{}$	None	None		✓			783.2.g.b	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
783.2.g.c	$783$	$2$	783.g	87.f	$4$	$40$	$20$	$6.252$		$_{}$	None	None		✓	✓		783.2.g.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
783.2.i.a	$783$	$2$	783.i	261.i	$6$	$56$	$28$	$6.252$		$_{}$	None	None			✓	✓	261.2.i.a	$4$	$0$	$0$	$0$	$-2$	$-2$			$\mathrm{SU}(2)[C_{6}]$
783.2.k.a	$783$	$2$	783.k	29.d	$7$	$6$	$1$	$6.252$	$\Q(\zeta_{14})$	$_{}$	None	None		✓			783.2.k.a	$2$	$0$	$-2$	$0$	$-8$	$-8$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
783.2.k.b	$783$	$2$	783.k	29.d	$7$	$6$	$1$	$6.252$	$\Q(\zeta_{14})$	$_{}$	None	None		✓			783.2.k.a	$2$	$0$	$2$	$0$	$8$	$-8$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots$
783.2.k.c	$783$	$2$	783.k	29.d	$7$	$54$	$9$	$6.252$		$_{}$	None	None		✓			783.2.k.c	$2$	$0$	$-4$	$0$	$-11$	$6$			$\mathrm{SU}(2)[C_{7}]$
783.2.k.d	$783$	$2$	783.k	29.d	$7$	$54$	$9$	$6.252$		$_{}$	None	None		✓			783.2.k.c	$2$	$0$	$4$	$0$	$11$	$6$			$\mathrm{SU}(2)[C_{7}]$
783.2.k.e	$783$	$2$	783.k	29.d	$7$	$60$	$10$	$6.252$		$_{}$	None	None		✓			783.2.k.e	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{7}]$
783.2.k.f	$783$	$2$	783.k	29.d	$7$	$60$	$10$	$6.252$		$_{}$	None	None		✓			783.2.k.f	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{7}]$
783.2.l.a	$783$	$2$	783.l	27.e	$9$	$234$	$39$	$6.252$		$_{}$	None	None		✓			783.2.l.a	$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$
783.2.l.b	$783$	$2$	783.l	27.e	$9$	$270$	$45$	$6.252$		$_{}$	None	None		✓	✓		783.2.l.b	$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$
783.2.m.a	$783$	$2$	783.m	261.l	$12$	$112$	$28$	$6.252$		$_{}$	None	None			✓	✓	261.2.l.a	$4$	$0$	$6$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$
783.2.p.a	$783$	$2$	783.p	29.e	$14$	$12$	$2$	$6.252$	$\Q(\zeta_{28})$	$_{}$	None	None		✓			783.2.p.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-\zeta_{28}+\zeta_{28}^{3}-\zeta_{28}^{5}+\zeta_{28}^{7}+\cdots)q^{2}+\cdots$
783.2.p.b	$783$	$2$	783.p	29.e	$14$	$108$	$18$	$6.252$		$_{}$	None	None		✓			783.2.p.b	$4$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{14}]$
783.2.p.c	$783$	$2$	783.p	29.e	$14$	$120$	$20$	$6.252$		$_{}$	None	None		✓	✓		783.2.p.c	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{14}]$
783.2.t.a	$783$	$2$	783.t	783.t	$18$	$528$	$88$	$6.252$		$_{}$	None	None		✓	✓	✓	783.2.t.a	$4$	$0$	$0$	$0$	$-12$	$-12$			$\mathrm{SU}(2)[C_{18}]$
783.2.u.a	$783$	$2$	783.u	261.q	$21$	$336$	$28$	$6.252$		$_{}$	None	None			✓	✓	261.2.q.a	$4$	$0$	$5$	$0$	$9$	$-5$			$\mathrm{SU}(2)[C_{21}]$
783.2.v.a	$783$	$2$	783.v	87.k	$28$	$240$	$20$	$6.252$		$_{}$	None	None		✓			783.2.v.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
783.2.v.b	$783$	$2$	783.v	87.k	$28$	$240$	$20$	$6.252$		$_{}$	None	None		✓			783.2.v.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
783.2.x.a	$783$	$2$	783.x	783.x	$36$	$1056$	$88$	$6.252$		$_{}$	None	None		✓	✓	✓	783.2.x.a	$4$	$0$	$-12$	$-12$	$0$	$-24$			$\mathrm{SU}(2)[C_{36}]$
783.2.ba.a	$783$	$2$	783.ba	261.u	$42$	$336$	$28$	$6.252$		$_{}$	None	None			✓	✓	261.2.u.a	$4$	$0$	$7$	$0$	$9$	$-5$			$\mathrm{SU}(2)[C_{42}]$
783.2.bc.a	$783$	$2$	783.bc	783.ac	$63$	$3168$	$88$	$6.252$		$_{}$	None	None		✓	✓	✓	783.2.bc.a	$4$	$0$	$-30$	$-30$	$-30$	$-30$			$\mathrm{SU}(2)[C_{63}]$
783.2.be.a	$783$	$2$	783.be	261.x	$84$	$672$	$28$	$6.252$		$_{}$	None	None			✓	✓	261.2.x.a	$4$	$0$	$36$	$0$	$42$	$-10$			$\mathrm{SU}(2)[C_{84}]$
783.2.bf.a	$783$	$2$	783.bf	783.af	$126$	$3168$	$88$	$6.252$		$_{}$	None	None		✓	✓	✓	783.2.bf.a	$4$	$0$	$-42$	$-42$	$-30$	$-30$			$\mathrm{SU}(2)[C_{126}]$
783.2.bj.a	$783$	$2$	783.bj	783.aj	$252$	$6336$	$88$	$6.252$		$_{}$	None	None		✓	✓	✓	783.2.bj.a	$4$	$0$	$-72$	$-72$	$-84$	$-60$			$\mathrm{SU}(2)[C_{252}]$
783.3.b.a	$783$	$3$	783.b	3.b	$2$	$18$	$18$	$21.335$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			783.3.b.a	$2$	$0$	$0$	$0$	$0$	$18$		$2\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$
783.3.b.b	$783$	$3$	783.b	3.b	$2$	$20$	$20$	$21.335$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			783.3.b.b	$2$	$0$	$0$	$0$	$0$	$-8$		$2\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{16}q^{5}+\cdots$
783.3.b.c	$783$	$3$	783.b	3.b	$2$	$36$	$36$	$21.335$		$_{}$	None	None		✓	✓		783.3.b.c	$2$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{2}]$
783.3.d.a	$783$	$3$	783.d	87.d	$2$	$6$	$6$	$21.335$	6.6.160016229.3	$_{}$	$\Q(\sqrt{-87}) $	None	✓	✓			783.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(4-\beta _{1}-\beta _{3}+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{7}+\cdots$
783.3.d.b	$783$	$3$	783.d	87.d	$2$	$6$	$6$	$21.335$	6.6.160016229.3	$_{}$	$\Q(\sqrt{-87}) $	None	✓	✓			783.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+(4-\beta _{1}+\beta _{2}+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{7}+\cdots$
783.3.d.c	$783$	$3$	783.d	87.d	$2$	$14$	$14$	$21.335$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			783.3.d.c	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}-\beta _{10}q^{5}-\beta _{6}q^{7}+\cdots$
783.3.d.d	$783$	$3$	783.d	87.d	$2$	$14$	$14$	$21.335$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			783.3.d.c	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(1-\beta _{4})q^{4}-\beta _{10}q^{5}-\beta _{6}q^{7}+\cdots$

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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.