LMFDB - Newform search results

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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 (45 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
3936.1.b.a	$3936$	$1$	3936.b	123.b	$2$	$16$	$16$	$1.964$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-41}) $	None		✓	✓	✓	3936.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{3}q^{3}+(\zeta_{32}^{2}+\zeta_{32}^{14})q^{5}+(-\zeta_{32}^{7}+\cdots)q^{7}+\cdots$
3936.1.m.a	$3936$	$1$	3936.m	984.m	$2$	$1$	$1$	$1.964$	$\Q$	$D_{3}$	$\Q(\sqrt{-246}) $	None	✓				984.1.m.a	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{5}+q^{9}-q^{13}+q^{15}-q^{17}+\cdots$
3936.1.m.b	$3936$	$1$	3936.m	984.m	$2$	$1$	$1$	$1.964$	$\Q$	$D_{3}$	$\Q(\sqrt{-246}) $	None	✓				984.1.m.a	$2$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}+q^{9}-q^{13}-q^{15}+q^{17}+\cdots$
3936.1.m.c	$3936$	$1$	3936.m	984.m	$2$	$1$	$1$	$1.964$	$\Q$	$D_{3}$	$\Q(\sqrt{-246}) $	None	✓				984.1.m.a	$2$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{5}+q^{9}+q^{13}-q^{15}+q^{17}+\cdots$
3936.1.m.d	$3936$	$1$	3936.m	984.m	$2$	$1$	$1$	$1.964$	$\Q$	$D_{3}$	$\Q(\sqrt{-246}) $	None	✓				984.1.m.a	$2$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{9}+q^{13}+q^{15}-q^{17}+\cdots$
3936.1.m.e	$3936$	$1$	3936.m	984.m	$2$	$4$	$4$	$1.964$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{82}) $			✓		984.1.m.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$
3936.1.cl.a	$3936$	$1$	3936.cl	984.ab	$8$	$4$	$1$	$1.964$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None					984.1.bb.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-q^{3}+q^{9}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+(-1+\cdots)q^{17}+\cdots$
3936.1.cl.b	$3936$	$1$	3936.cl	984.ab	$8$	$4$	$1$	$1.964$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None					984.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
3936.1.fx.a	$3936$	$1$	3936.fx	984.bj	$40$	$16$	$1$	$1.964$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-2}) $	None					984.1.cj.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{17}q^{3}-\zeta_{40}^{14}q^{9}+(-\zeta_{40}^{15}+\cdots)q^{11}+\cdots$
3936.1.fx.b	$3936$	$1$	3936.fx	984.bj	$40$	$16$	$1$	$1.964$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-2}) $	None					984.1.cj.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\zeta_{40}^{8}q^{3}+\zeta_{40}^{16}q^{9}+(\zeta_{40}^{15}+\zeta_{40}^{18}+\cdots)q^{11}+\cdots$
3936.2.a.a	$3936$	$2$	3936.a	1.a	$1$	$1$	$1$	$31.429$	$\Q$	$_{}$	None	None	✓	✓			3936.2.a.a	$1$	$1$	$0$	$-1$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
3936.2.a.b	$3936$	$2$	3936.a	1.a	$1$	$1$	$1$	$31.429$	$\Q$	$_{}$	None	None	✓	✓			3936.2.a.b	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-5q^{13}+\cdots$
3936.2.a.c	$3936$	$2$	3936.a	1.a	$1$	$1$	$1$	$31.429$	$\Q$	$_{}$	None	None	✓	✓			3936.2.a.c	$1$	$0$	$0$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
3936.2.a.d	$3936$	$2$	3936.a	1.a	$1$	$1$	$1$	$31.429$	$\Q$	$_{}$	None	None	✓	✓			3936.2.a.a	$1$	$0$	$0$	$1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
3936.2.a.e	$3936$	$2$	3936.a	1.a	$1$	$1$	$1$	$31.429$	$\Q$	$_{}$	None	None	✓	✓			3936.2.a.b	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-5q^{13}+\cdots$
3936.2.a.f	$3936$	$2$	3936.a	1.a	$1$	$1$	$1$	$31.429$	$\Q$	$_{}$	None	None	✓	✓			3936.2.a.c	$1$	$0$	$0$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
3936.2.a.g	$3936$	$2$	3936.a	1.a	$1$	$3$	$3$	$31.429$	3.3.148.1	$_{}$	None	None	✓	✓			3936.2.a.g	$1$	$1$	$0$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$
3936.2.a.h	$3936$	$2$	3936.a	1.a	$1$	$3$	$3$	$31.429$	3.3.148.1	$_{}$	None	None	✓	✓			3936.2.a.g	$1$	$1$	$0$	$3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots$
3936.2.a.i	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.15188.1	$_{}$	None	None	✓	✓			3936.2.a.i	$1$	$1$	$0$	$-4$	$-4$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{3})q^{5}+(1-\beta _{2})q^{7}+\cdots$
3936.2.a.j	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.202932.1	$_{}$	None	None	✓	✓	✓		3936.2.a.j	$1$	$1$	$0$	$-4$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots$
3936.2.a.k	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.17428.1	$_{}$	None	None	✓	✓			3936.2.a.k	$1$	$0$	$0$	$-4$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
3936.2.a.l	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.8468.1	$_{}$	None	None	✓	✓			3936.2.a.l	$1$	$0$	$0$	$-4$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{3}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots$
3936.2.a.m	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.15188.1	$_{}$	None	None	✓	✓			3936.2.a.i	$1$	$1$	$0$	$4$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{3})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
3936.2.a.n	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.202932.1	$_{}$	None	None	✓	✓			3936.2.a.j	$1$	$0$	$0$	$4$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots$
3936.2.a.o	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.17428.1	$_{}$	None	None	✓	✓	✓		3936.2.a.k	$1$	$1$	$0$	$4$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
3936.2.a.p	$3936$	$2$	3936.a	1.a	$1$	$4$	$4$	$31.429$	4.4.8468.1	$_{}$	None	None	✓	✓			3936.2.a.l	$1$	$1$	$0$	$4$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{3}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+q^{9}+\cdots$
3936.2.a.q	$3936$	$2$	3936.a	1.a	$1$	$5$	$5$	$31.429$	5.5.6852676.1	$_{}$	None	None	✓	✓	✓		3936.2.a.q	$1$	$0$	$0$	$-5$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
3936.2.a.r	$3936$	$2$	3936.a	1.a	$1$	$5$	$5$	$31.429$	5.5.6852676.1	$_{}$	None	None	✓	✓			3936.2.a.q	$1$	$0$	$0$	$5$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
3936.2.a.s	$3936$	$2$	3936.a	1.a	$1$	$6$	$6$	$31.429$	6.6.121506628.1	$_{}$	None	None	✓	✓	✓		3936.2.a.s	$1$	$1$	$0$	$-6$	$3$	$-8$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{4}q^{5}+(-1+\beta _{3})q^{7}+q^{9}+\cdots$
3936.2.a.t	$3936$	$2$	3936.a	1.a	$1$	$6$	$6$	$31.429$	6.6.121506628.1	$_{}$	None	None	✓	✓	✓		3936.2.a.s	$1$	$0$	$0$	$6$	$3$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{4}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
3936.2.a.u	$3936$	$2$	3936.a	1.a	$1$	$7$	$7$	$31.429$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		3936.2.a.u	$1$	$0$	$0$	$-7$	$6$	$-8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
3936.2.a.v	$3936$	$2$	3936.a	1.a	$1$	$7$	$7$	$31.429$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		3936.2.a.u	$1$	$0$	$0$	$7$	$6$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots$
3936.2.e.a	$3936$	$2$	3936.e	328.g	$2$	$42$	$42$	$31.429$		$_{}$	None	None					984.2.e.a	$2$	$0$	$0$	$-42$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3936.2.e.b	$3936$	$2$	3936.e	328.g	$2$	$42$	$42$	$31.429$		$_{}$	None	None					984.2.e.a	$2$	$0$	$0$	$42$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3936.2.f.a	$3936$	$2$	3936.f	8.b	$2$	$40$	$40$	$31.429$		$_{}$	None	None					984.2.f.a	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
3936.2.f.b	$3936$	$2$	3936.f	8.b	$2$	$40$	$40$	$31.429$		$_{}$	None	None					984.2.f.b	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
3936.2.j.a	$3936$	$2$	3936.j	41.b	$2$	$2$	$2$	$31.429$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			3936.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+4 i q^{7}-q^{9}-3 i q^{11}+\cdots$
3936.2.j.b	$3936$	$2$	3936.j	41.b	$2$	$2$	$2$	$31.429$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			3936.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-4 i q^{7}-q^{9}+3 i q^{11}+\cdots$
3936.2.j.c	$3936$	$2$	3936.j	41.b	$2$	$2$	$2$	$31.429$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			3936.2.j.c	$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+3 q^{5}-2 i q^{7}-q^{9}-5 i q^{13}+\cdots$
3936.2.j.d	$3936$	$2$	3936.j	41.b	$2$	$2$	$2$	$31.429$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			3936.2.j.c	$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+3 q^{5}-2 i q^{7}-q^{9}+5 i q^{13}+\cdots$
3936.2.j.e	$3936$	$2$	3936.j	41.b	$2$	$4$	$4$	$31.429$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			3936.2.j.e	$4$	$0$	$0$	$0$	$8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+2q^{5}+2\beta _{1}q^{7}-q^{9}+3\beta _{1}q^{11}+\cdots$
3936.2.j.f	$3936$	$2$	3936.j	41.b	$2$	$8$	$8$	$31.429$	8.0.$\cdots$.7	$_{}$	None	None		✓			3936.2.j.f	$4$	$0$	$0$	$0$	$-16$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-2q^{5}-2\beta _{2}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots$
3936.2.j.g	$3936$	$2$	3936.j	41.b	$2$	$20$	$20$	$31.429$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			3936.2.j.g	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}-\beta _{7}q^{5}+\beta _{16}q^{7}-q^{9}+\beta _{9}q^{11}+\cdots$
3936.2.j.h	$3936$	$2$	3936.j	41.b	$2$	$22$	$22$	$31.429$		$_{}$	None	None		✓			3936.2.j.h	$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
3936.2.j.i	$3936$	$2$	3936.j	41.b	$2$	$22$	$22$	$31.429$		$_{}$	None	None		✓			3936.2.j.h	$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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.