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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 165 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
775.1.c.a	$775$	$1$	775.c	155.c	$2$	$2$	$2$	$0.387$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-iq^{7}-iq^{8}-q^{9}-q^{14}+\cdots$
775.1.d.a	$775$	$1$	775.d	31.b	$2$	$1$	$1$	$0.387$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{9}+q^{16}+2q^{19}-q^{31}+\cdots$
775.1.d.b	$775$	$1$	775.d	31.b	$2$	$1$	$1$	$0.387$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$1$		$1$		$q+q^{2}+q^{7}-q^{8}+q^{9}+q^{14}-q^{16}+\cdots$
775.1.d.c	$775$	$1$	775.d	31.b	$2$	$2$	$2$	$0.387$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{2}+2q^{4}+\beta q^{7}-\beta q^{8}+q^{9}+\cdots$
775.1.w.a	$775$	$1$	775.w	775.w	$10$	$4$	$1$	$0.387$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$3$	$0$	$-1$	$-2$		$1$		$q+(1-\zeta_{10})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2})q^{4}+\cdots$
775.1.w.b	$775$	$1$	775.w	775.w	$10$	$8$	$2$	$0.387$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-3$	$0$	$1$	$2$		$1$		$q+(-\zeta_{30}^{5}-\zeta_{30}^{13})q^{2}+(-\zeta_{30}^{3}+\cdots)q^{4}+\cdots$
775.1.z.a	$775$	$1$	775.z	775.z	$10$	$4$	$1$	$0.387$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-5$	$0$	$1$	$0$		$1$		$q+(-1+\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
775.1.z.b	$775$	$1$	775.z	775.z	$10$	$8$	$2$	$0.387$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$5$	$0$	$-1$	$0$		$1$		$q+(\zeta_{30}^{2}-\zeta_{30}^{10})q^{2}+(\zeta_{30}^{4}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
775.2.a.a	$775$	$2$	775.a	1.a	$1$	$1$	$1$	$6.188$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-2q^{9}-4q^{11}-2q^{12}+\cdots$
775.2.a.b	$775$	$2$	775.a	1.a	$1$	$1$	$1$	$6.188$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-2q^{6}-4q^{7}-3q^{8}+\cdots$
775.2.a.c	$775$	$2$	775.a	1.a	$1$	$1$	$1$	$6.188$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots$
775.2.a.d	$775$	$2$	775.a	1.a	$1$	$2$	$2$	$6.188$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+2\beta q^{3}+(-1+\beta )q^{4}+(-2+\cdots)q^{6}+\cdots$
775.2.a.e	$775$	$2$	775.a	1.a	$1$	$4$	$4$	$6.188$	4.4.8468.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots$
775.2.a.f	$775$	$2$	775.a	1.a	$1$	$4$	$4$	$6.188$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1-\beta _{2}+\cdots)q^{6}+\cdots$
775.2.a.g	$775$	$2$	775.a	1.a	$1$	$4$	$4$	$6.188$	4.4.20308.1	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots$
775.2.a.h	$775$	$2$	775.a	1.a	$1$	$5$	$5$	$6.188$	5.5.144209.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
775.2.a.i	$775$	$2$	775.a	1.a	$1$	$5$	$5$	$6.188$	5.5.205225.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$-1$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{3}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
775.2.a.j	$775$	$2$	775.a	1.a	$1$	$5$	$5$	$6.188$	5.5.205225.1	$_{}$	None	None	✓	$1$	$0$	$4$	$1$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
775.2.a.k	$775$	$2$	775.a	1.a	$1$	$5$	$5$	$6.188$	5.5.144209.1	$_{}$	None	None	✓	$1$	$0$	$4$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
775.2.a.l	$775$	$2$	775.a	1.a	$1$	$10$	$10$	$6.188$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots$
775.2.b.a	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots$
775.2.b.b	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-4iq^{7}+\cdots$
775.2.b.c	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+2q^{4}+2q^{9}-4q^{11}-2iq^{12}+\cdots$
775.2.b.d	$775$	$2$	775.b	5.b	$2$	$4$	$4$	$6.188$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+2\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots$
775.2.b.e	$775$	$2$	775.b	5.b	$2$	$8$	$8$	$6.188$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-2+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
775.2.b.f	$775$	$2$	775.b	5.b	$2$	$8$	$8$	$6.188$	8.0.4589249536.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{4})q^{4}+(-1+\cdots)q^{6}+\cdots$
775.2.b.g	$775$	$2$	775.b	5.b	$2$	$10$	$10$	$6.188$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{4}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{8})q^{3}+(-1+\cdots)q^{4}+\cdots$
775.2.b.h	$775$	$2$	775.b	5.b	$2$	$10$	$10$	$6.188$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{6}+\cdots)q^{4}+\cdots$
775.2.e.a	$775$	$2$	775.e	31.c	$3$	$2$	$1$	$6.188$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-4$	$2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{2}+(2-2\zeta_{6})q^{3}+2q^{4}+(-4+\cdots)q^{6}+\cdots$
775.2.e.b	$775$	$2$	775.e	31.c	$3$	$2$	$1$	$6.188$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$4$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2q^{2}+(2-2\zeta_{6})q^{3}+2q^{4}+(4-4\zeta_{6})q^{6}+\cdots$
775.2.e.c	$775$	$2$	775.e	31.c	$3$	$4$	$2$	$6.188$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$-2$	$-3$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
775.2.e.d	$775$	$2$	775.e	31.c	$3$	$4$	$2$	$6.188$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$2$	$3$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots$
775.2.e.e	$775$	$2$	775.e	31.c	$3$	$4$	$2$	$6.188$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$4$	$-2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
775.2.e.f	$775$	$2$	775.e	31.c	$3$	$8$	$4$	$6.188$	8.0.42575625.1	$_{}$	None	None		$2$	$0$	$-2$	$1$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(-1-\beta _{1}+2\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
775.2.e.g	$775$	$2$	775.e	31.c	$3$	$8$	$4$	$6.188$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$-3$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
775.2.e.h	$775$	$2$	775.e	31.c	$3$	$18$	$9$	$6.188$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+\beta _{14}q^{3}+(1-\beta _{2})q^{4}+(\beta _{13}+\cdots)q^{6}+\cdots$
775.2.e.i	$775$	$2$	775.e	31.c	$3$	$18$	$9$	$6.188$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+(-\beta _{5}+\beta _{14})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
775.2.e.j	$775$	$2$	775.e	31.c	$3$	$28$	$14$	$6.188$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
775.2.f.a	$775$	$2$	775.f	155.f	$4$	$4$	$2$	$6.188$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
775.2.f.b	$775$	$2$	775.f	155.f	$4$	$4$	$2$	$6.188$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
775.2.f.c	$775$	$2$	775.f	155.f	$4$	$8$	$4$	$6.188$	8.0.3317760000.2	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}-\beta _{3}q^{3}-4\beta _{2}q^{4}-\beta _{7}q^{6}+\cdots$
775.2.f.d	$775$	$2$	775.f	155.f	$4$	$8$	$4$	$6.188$	8.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-155}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{3}q^{3}+2\beta _{4}q^{4}+(-3\beta _{4}-\beta _{7})q^{9}+\cdots$
775.2.f.e	$775$	$2$	775.f	155.f	$4$	$12$	$6$	$6.188$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 5^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{4}q^{2}+(2\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\beta _{9}+\cdots)q^{7}+\cdots$
775.2.f.f	$775$	$2$	775.f	155.f	$4$	$16$	$8$	$6.188$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$12$		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{7}+\cdots)q^{6}+\cdots$
775.2.f.g	$775$	$2$	775.f	155.f	$4$	$40$	$20$	$6.188$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
775.2.h.a	$775$	$2$	775.h	775.h	$5$	$312$	$78$	$6.188$		$_{}$	None	None		$2$	$0$	$-1$	$3$	$-6$	$-8$			$\mathrm{SU}(2)[C_{5}]$
775.2.i.a	$775$	$2$	775.i	775.i	$5$	$312$	$78$	$6.188$		$_{}$	None	None		$2$	$0$	$-1$	$-2$	$-6$	$2$			$\mathrm{SU}(2)[C_{5}]$
775.2.j.a	$775$	$2$	775.j	25.d	$5$	$4$	$1$	$6.188$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$-2$	$-6$	$-5$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
775.2.j.b	$775$	$2$	775.j	25.d	$5$	$140$	$35$	$6.188$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$-3$	$-2$			$\mathrm{SU}(2)[C_{5}]$
775.2.j.c	$775$	$2$	775.j	25.d	$5$	$160$	$40$	$6.188$		$_{}$	None	None		$2$	$0$	$1$	$6$	$2$	$-10$			$\mathrm{SU}(2)[C_{5}]$

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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.