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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 323 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
624.1.l.a	$624$	$1$	624.l	39.d	$2$	$1$	$1$	$0.311$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{9}-q^{13}-q^{25}+q^{27}-q^{39}+\cdots$
624.1.bd.a	$624$	$1$	624.bd	156.l	$4$	$2$	$1$	$0.311$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-iq^{3}+(-1-i)q^{7}-q^{9}-iq^{13}+\cdots$
624.1.bd.b	$624$	$1$	624.bd	156.l	$4$	$2$	$1$	$0.311$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+iq^{3}+(1+i)q^{7}-q^{9}-iq^{13}+(-1+\cdots)q^{19}+\cdots$
624.1.bi.a	$624$	$1$	624.bi	624.ai	$4$	$8$	$4$	$0.311$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
624.1.bs.a	$624$	$1$	624.bs	39.i	$6$	$2$	$1$	$0.311$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
624.1.cb.a	$624$	$1$	624.cb	39.h	$6$	$2$	$1$	$0.311$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$		$1$		$q-\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
624.1.cp.a	$624$	$1$	624.cp	156.v	$12$	$4$	$1$	$0.311$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}q^{3}+(-\zeta_{12}^{3}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
624.1.cp.b	$624$	$1$	624.cp	156.v	$12$	$4$	$1$	$0.311$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{12}q^{3}+(\zeta_{12}^{3}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
624.2.a.a	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$
624.2.a.b	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+q^{13}-6q^{17}+\cdots$
624.2.a.c	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-6q^{11}-q^{13}+2q^{17}+\cdots$
624.2.a.d	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+q^{13}-2q^{15}+\cdots$
624.2.a.e	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
624.2.a.f	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}+q^{13}-2q^{15}+\cdots$
624.2.a.g	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$
624.2.a.h	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
624.2.a.i	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
624.2.a.j	$624$	$2$	624.a	1.a	$1$	$1$	$1$	$4.983$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{9}+2q^{11}-q^{13}+\cdots$
624.2.a.k	$624$	$2$	624.a	1.a	$1$	$2$	$2$	$4.983$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots$
624.2.c.a	$624$	$2$	624.c	13.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+iq^{5}+iq^{7}+q^{9}+(-3-i)q^{13}+\cdots$
624.2.c.b	$624$	$2$	624.c	13.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots$
624.2.c.c	$624$	$2$	624.c	13.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots$
624.2.c.d	$624$	$2$	624.c	13.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+iq^{5}-2iq^{7}+q^{9}+3iq^{11}+\cdots$
624.2.c.e	$624$	$2$	624.c	13.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots$
624.2.c.f	$624$	$2$	624.c	13.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots$
624.2.c.g	$624$	$2$	624.c	13.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+iq^{7}+q^{9}+iq^{11}+(3-i)q^{13}+\cdots$
624.2.d.a	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots$
624.2.d.b	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}-\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
624.2.d.c	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{3}+2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots$
624.2.d.d	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{9}+\cdots$
624.2.d.e	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+2\beta )q^{9}+\cdots$
624.2.d.f	$624$	$2$	624.d	12.b	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
624.2.d.g	$624$	$2$	624.d	12.b	$2$	$4$	$4$	$4.983$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
624.2.d.h	$624$	$2$	624.d	12.b	$2$	$4$	$4$	$4.983$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+3q^{9}+2\beta _{2}q^{11}+\cdots$
624.2.d.i	$624$	$2$	624.d	12.b	$2$	$4$	$4$	$4.983$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
624.2.n.a	$624$	$2$	624.n	156.h	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$1$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}-4q^{7}-3q^{9}+(1+2\zeta_{6})q^{13}+\cdots$
624.2.n.b	$624$	$2$	624.n	156.h	$2$	$2$	$2$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}+4q^{7}-3q^{9}+(1-2\zeta_{6})q^{13}+\cdots$
624.2.n.c	$624$	$2$	624.n	156.h	$2$	$4$	$4$	$4.983$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$
624.2.n.d	$624$	$2$	624.n	156.h	$2$	$4$	$4$	$4.983$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$
624.2.n.e	$624$	$2$	624.n	156.h	$2$	$8$	$8$	$4.983$	8.0.170772624.1	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+(\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots$
624.2.n.f	$624$	$2$	624.n	156.h	$2$	$8$	$8$	$4.983$	8.0.170772624.1	$_{}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(\beta _{3}+\beta _{5})q^{5}+(\beta _{3}+\beta _{5})q^{7}+\cdots$
624.2.q.a	$624$	$2$	624.q	13.c	$3$	$2$	$1$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-1$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
624.2.q.b	$624$	$2$	624.q	13.c	$3$	$2$	$1$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
624.2.q.c	$624$	$2$	624.q	13.c	$3$	$2$	$1$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
624.2.q.d	$624$	$2$	624.q	13.c	$3$	$2$	$1$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
624.2.q.e	$624$	$2$	624.q	13.c	$3$	$2$	$1$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
624.2.q.f	$624$	$2$	624.q	13.c	$3$	$2$	$1$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+3q^{5}-\zeta_{6}q^{9}+(3+\zeta_{6})q^{13}+\cdots$
624.2.q.g	$624$	$2$	624.q	13.c	$3$	$2$	$1$	$4.983$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
624.2.q.h	$624$	$2$	624.q	13.c	$3$	$4$	$2$	$4.983$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
624.2.q.i	$624$	$2$	624.q	13.c	$3$	$4$	$2$	$4.983$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-4$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1})q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{9}+\cdots$

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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.