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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 (39 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
3552.1.i.a	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓				888.1.i.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{7}+q^{9}+q^{11}-q^{13}-q^{17}+\cdots$
3552.1.i.b	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓				888.1.i.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{7}+q^{9}+q^{11}+q^{13}+q^{17}+\cdots$
3552.1.i.c	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓				888.1.i.a	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+q^{3}+q^{7}+q^{9}-q^{11}-q^{13}+q^{17}+\cdots$
3552.1.i.d	$3552$	$1$	3552.i	888.i	$2$	$1$	$1$	$1.773$	$\Q$	$D_{3}$	$\Q(\sqrt{-222}) $	None	✓				888.1.i.a	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+q^{3}+q^{7}+q^{9}-q^{11}+q^{13}-q^{17}+\cdots$
3552.1.i.e	$3552$	$1$	3552.i	888.i	$2$	$8$	$8$	$1.773$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None			✓		888.1.i.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$		$q-\zeta_{16}^{4}q^{3}+(-\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots$
3552.1.bw.a	$3552$	$1$	3552.bw	111.i	$6$	$4$	$2$	$1.773$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓			3552.1.bw.a	$4$	$0$	$0$	$-2$	$0$	$2$		$1$		$q-\beta _{2}q^{3}+\beta _{2}q^{7}+(-1+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$
3552.1.bw.b	$3552$	$1$	3552.bw	111.i	$6$	$4$	$2$	$1.773$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓			3552.1.bw.a	$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+\beta _{2}q^{3}-\beta _{2}q^{7}+(-1+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$
3552.1.ce.a	$3552$	$1$	3552.ce	3552.be	$8$	$32$	$8$	$1.773$	$\Q(\zeta_{64})$	$D_{32}$	$\Q(\sqrt{-111}) $	None		✓	✓	✓	3552.1.ce.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{64}^{27}q^{2}+\zeta_{64}^{4}q^{3}-\zeta_{64}^{22}q^{4}+\cdots$
3552.2.a.a	$3552$	$2$	3552.a	1.a	$1$	$1$	$1$	$28.363$	$\Q$	$_{}$	None	None	✓	✓			3552.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots$
3552.2.a.b	$3552$	$2$	3552.a	1.a	$1$	$1$	$1$	$28.363$	$\Q$	$_{}$	None	None	✓	✓			3552.2.a.b	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
3552.2.a.c	$3552$	$2$	3552.a	1.a	$1$	$1$	$1$	$28.363$	$\Q$	$_{}$	None	None	✓	✓			3552.2.a.c	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
3552.2.a.d	$3552$	$2$	3552.a	1.a	$1$	$1$	$1$	$28.363$	$\Q$	$_{}$	None	None	✓	✓			3552.2.a.c	$1$	$0$	$0$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
3552.2.a.e	$3552$	$2$	3552.a	1.a	$1$	$1$	$1$	$28.363$	$\Q$	$_{}$	None	None	✓	✓			3552.2.a.b	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
3552.2.a.f	$3552$	$2$	3552.a	1.a	$1$	$1$	$1$	$28.363$	$\Q$	$_{}$	None	None	✓	✓			3552.2.a.a	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots$
3552.2.a.g	$3552$	$2$	3552.a	1.a	$1$	$3$	$3$	$28.363$	3.3.148.1	$_{}$	None	None	✓	✓			3552.2.a.g	$1$	$1$	$0$	$-3$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
3552.2.a.h	$3552$	$2$	3552.a	1.a	$1$	$3$	$3$	$28.363$	3.3.148.1	$_{}$	None	None	✓	✓			3552.2.a.h	$1$	$1$	$0$	$-3$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots$
3552.2.a.i	$3552$	$2$	3552.a	1.a	$1$	$3$	$3$	$28.363$	3.3.148.1	$_{}$	None	None	✓	✓			3552.2.a.i	$1$	$1$	$0$	$-3$	$4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2-2\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
3552.2.a.j	$3552$	$2$	3552.a	1.a	$1$	$3$	$3$	$28.363$	3.3.148.1	$_{}$	None	None	✓	✓			3552.2.a.h	$1$	$1$	$0$	$3$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
3552.2.a.k	$3552$	$2$	3552.a	1.a	$1$	$3$	$3$	$28.363$	3.3.148.1	$_{}$	None	None	✓	✓			3552.2.a.g	$1$	$1$	$0$	$3$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
3552.2.a.l	$3552$	$2$	3552.a	1.a	$1$	$3$	$3$	$28.363$	3.3.148.1	$_{}$	None	None	✓	✓			3552.2.a.i	$1$	$0$	$0$	$3$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2-2\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
3552.2.a.m	$3552$	$2$	3552.a	1.a	$1$	$4$	$4$	$28.363$	4.4.97300.1	$_{}$	None	None	✓	✓			3552.2.a.m	$1$	$0$	$0$	$-4$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots$
3552.2.a.n	$3552$	$2$	3552.a	1.a	$1$	$4$	$4$	$28.363$	4.4.11348.1	$_{}$	None	None	✓	✓			3552.2.a.n	$1$	$0$	$0$	$-4$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
3552.2.a.o	$3552$	$2$	3552.a	1.a	$1$	$4$	$4$	$28.363$	4.4.15188.1	$_{}$	None	None	✓	✓	✓		3552.2.a.o	$1$	$1$	$0$	$-4$	$2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{1})q^{7}+\cdots$
3552.2.a.p	$3552$	$2$	3552.a	1.a	$1$	$4$	$4$	$28.363$	4.4.97300.1	$_{}$	None	None	✓	✓	✓		3552.2.a.m	$1$	$1$	$0$	$4$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots$
3552.2.a.q	$3552$	$2$	3552.a	1.a	$1$	$4$	$4$	$28.363$	4.4.11348.1	$_{}$	None	None	✓	✓	✓		3552.2.a.n	$1$	$1$	$0$	$4$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
3552.2.a.r	$3552$	$2$	3552.a	1.a	$1$	$4$	$4$	$28.363$	4.4.15188.1	$_{}$	None	None	✓	✓			3552.2.a.o	$1$	$0$	$0$	$4$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+q^{9}+\cdots$
3552.2.a.s	$3552$	$2$	3552.a	1.a	$1$	$5$	$5$	$28.363$	5.5.792644.1	$_{}$	None	None	✓	✓	✓		3552.2.a.s	$1$	$0$	$0$	$-5$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
3552.2.a.t	$3552$	$2$	3552.a	1.a	$1$	$5$	$5$	$28.363$	5.5.792644.1	$_{}$	None	None	✓	✓	✓		3552.2.a.s	$1$	$0$	$0$	$5$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
3552.2.a.u	$3552$	$2$	3552.a	1.a	$1$	$7$	$7$	$28.363$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		3552.2.a.u	$1$	$0$	$0$	$-7$	$2$	$2$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
3552.2.a.v	$3552$	$2$	3552.a	1.a	$1$	$7$	$7$	$28.363$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		3552.2.a.u	$1$	$0$	$0$	$7$	$2$	$-2$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots$
3552.2.f.a	$3552$	$2$	3552.f	8.b	$2$	$28$	$28$	$28.363$		$_{}$	None	None					888.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3552.2.f.b	$3552$	$2$	3552.f	8.b	$2$	$44$	$44$	$28.363$		$_{}$	None	None			✓		888.2.f.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3552.2.h.a	$3552$	$2$	3552.h	37.b	$2$	$6$	$6$	$28.363$	6.0.3356224.1	$_{}$	None	None		✓			3552.2.h.a	$2$	$0$	$0$	$-6$	$0$	$-8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+q^{9}+\cdots$
3552.2.h.b	$3552$	$2$	3552.h	37.b	$2$	$6$	$6$	$28.363$	6.0.3356224.1	$_{}$	None	None		✓			3552.2.h.a	$2$	$0$	$0$	$6$	$0$	$8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
3552.2.h.c	$3552$	$2$	3552.h	37.b	$2$	$12$	$12$	$28.363$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			3552.2.h.c	$2$	$0$	$0$	$-12$	$0$	$8$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{1}q^{5}+(1+\beta _{9})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
3552.2.h.d	$3552$	$2$	3552.h	37.b	$2$	$12$	$12$	$28.363$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			3552.2.h.c	$2$	$0$	$0$	$12$	$0$	$-8$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{9})q^{7}+q^{9}+\cdots$
3552.2.h.e	$3552$	$2$	3552.h	37.b	$2$	$20$	$20$	$28.363$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			3552.2.h.e	$2$	$0$	$0$	$-20$	$0$	$-8$		$2^{23}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{15}q^{5}-\beta _{3}q^{7}+q^{9}+\beta _{2}q^{11}+\cdots$
3552.2.h.f	$3552$	$2$	3552.h	37.b	$2$	$20$	$20$	$28.363$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			3552.2.h.e	$2$	$0$	$0$	$20$	$0$	$8$		$2^{23}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{15}q^{5}+\beta _{3}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots$
3552.2.o.a	$3552$	$2$	3552.o	296.e	$2$	$76$	$76$	$28.363$		$_{}$	None	None			✓	✓	888.2.o.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$

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Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
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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.