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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 (32 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
137.2.a.a	$137$	$2$	137.a	1.a	$1$	$4$	$4$	$1.094$	$\Q(\sqrt{22 +2 \sqrt{5}})$	None	✓	✓	✓	✓	137.2.a.a	$1$	$1$	$-3$	$-5$	$-2$	$-13$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$
137.2.a.b	$137$	$2$	137.a	1.a	$1$	$7$	$7$	$1.094$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	137.2.a.b	$1$	$0$	$0$	$3$	$-2$	$15$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
137.2.b.a	$137$	$2$	137.b	137.b	$2$	$10$	$10$	$1.094$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓	✓	✓	137.2.b.a	$2$	$0$	$-4$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-\beta _{1}q^{3}+(\beta _{6}-\beta _{9})q^{4}-\beta _{3}q^{5}+\cdots$
137.2.c.a	$137$	$2$	137.c	137.c	$4$	$22$	$11$	$1.094$		None		✓	✓	✓	137.2.c.a	$2$	$0$	$0$	$-6$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
137.2.e.a	$137$	$2$	137.e	137.e	$17$	$160$	$10$	$1.094$		None		✓	✓	✓	137.2.e.a	$2$	$0$	$-11$	$-11$	$-7$	$-28$			$\mathrm{SU}(2)[C_{17}]$
137.2.f.a	$137$	$2$	137.f	137.f	$34$	$160$	$10$	$1.094$		None		✓	✓	✓	137.2.f.a	$2$	$0$	$-13$	$-17$	$-17$	$-2$			$\mathrm{SU}(2)[C_{34}]$
137.2.g.a	$137$	$2$	137.g	137.g	$68$	$352$	$11$	$1.094$		None		✓	✓	✓	137.2.g.a	$2$	$0$	$-34$	$-28$	$-30$	$-34$			$\mathrm{SU}(2)[C_{68}]$
137.3.d.a	$137$	$3$	137.d	137.d	$8$	$88$	$22$	$3.733$		None		✓	✓	✓	137.3.d.a	$2$	$0$	$-4$	$0$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
137.3.h.a	$137$	$3$	137.h	137.h	$136$	$1408$	$22$	$3.733$		None		✓	✓	✓	137.3.h.a	$2$	$0$	$-64$	$-68$	$-64$	$-64$			$\mathrm{SU}(2)[C_{136}]$
137.4.a.a	$137$	$4$	137.a	1.a	$1$	$15$	$15$	$8.083$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓	✓	✓	137.4.a.a	$1$	$1$	$-6$	$-18$	$-20$	$-122$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(3+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
137.4.a.b	$137$	$4$	137.a	1.a	$1$	$19$	$19$	$8.083$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	✓	✓	✓	137.4.a.b	$1$	$0$	$6$	$18$	$10$	$130$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(5+\beta _{2})q^{4}+\cdots$
137.4.b.a	$137$	$4$	137.b	137.b	$2$	$34$	$34$	$8.083$		None		✓	✓	✓	137.4.b.a	$2$	$0$	$-4$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{2}]$
137.4.c.a	$137$	$4$	137.c	137.c	$4$	$66$	$33$	$8.083$		None		✓	✓	✓	137.4.c.a	$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
137.4.e.a	$137$	$4$	137.e	137.e	$17$	$544$	$34$	$8.083$		None		✓	✓	✓	137.4.e.a	$2$	$0$	$-17$	$-17$	$-7$	$-59$			$\mathrm{SU}(2)[C_{17}]$
137.4.f.a	$137$	$4$	137.f	137.f	$34$	$544$	$34$	$8.083$		None		✓	✓	✓	137.4.f.a	$2$	$0$	$-13$	$-17$	$-17$	$29$			$\mathrm{SU}(2)[C_{34}]$
137.4.g.a	$137$	$4$	137.g	137.g	$68$	$1056$	$33$	$8.083$		None		✓	✓	✓	137.4.g.a	$2$	$0$	$-34$	$-34$	$-30$	$-34$			$\mathrm{SU}(2)[C_{68}]$
137.5.d.a	$137$	$5$	137.d	137.d	$8$	$180$	$45$	$14.162$		None		✓	✓	✓	137.5.d.a	$2$	$0$	$-16$	$0$	$-64$	$-4$			$\mathrm{SU}(2)[C_{8}]$
137.5.h.a	$137$	$5$	137.h	137.h	$136$	$2880$	$45$	$14.162$		None		✓	✓	✓	137.5.h.a	$2$	$0$	$-52$	$-68$	$-4$	$-64$			$\mathrm{SU}(2)[C_{136}]$
137.6.a.a	$137$	$6$	137.a	1.a	$1$	$26$	$26$	$21.973$		None	✓	✓	✓	✓	137.6.a.a	$1$	$1$	$-12$	$-45$	$-50$	$-873$	$+$		$\mathrm{SU}(2)$
137.6.a.b	$137$	$6$	137.a	1.a	$1$	$30$	$30$	$21.973$		None	✓	✓	✓	✓	137.6.a.b	$1$	$0$	$12$	$63$	$100$	$891$	$-$		$\mathrm{SU}(2)$
137.6.b.a	$137$	$6$	137.b	137.b	$2$	$56$	$56$	$21.973$		None		✓	✓	✓	137.6.b.a	$2$	$0$	$8$	$0$	$0$	$-22$			$\mathrm{SU}(2)[C_{2}]$
137.8.a.a	$137$	$8$	137.a	1.a	$1$	$38$	$38$	$42.797$		None	✓	✓	✓	✓	137.8.a.a	$1$	$1$	$-24$	$-189$	$-500$	$-6029$	$-$		$\mathrm{SU}(2)$
137.8.a.b	$137$	$8$	137.a	1.a	$1$	$42$	$42$	$42.797$		None	✓	✓	✓	✓	137.8.a.b	$1$	$0$	$24$	$135$	$250$	$6319$	$+$		$\mathrm{SU}(2)$
137.8.b.a	$137$	$8$	137.b	137.b	$2$	$80$	$80$	$42.797$		None		✓	✓	✓	137.8.b.a	$2$	$0$	$-16$	$0$	$0$	$-294$			$\mathrm{SU}(2)[C_{2}]$
137.10.a.a	$137$	$10$	137.a	1.a	$1$	$49$	$49$	$70.560$		None	✓	✓	✓	✓	137.10.a.a	$1$	$1$	$-48$	$-486$	$-1250$	$-47526$	$+$		$\mathrm{SU}(2)$
137.10.a.b	$137$	$10$	137.a	1.a	$1$	$53$	$53$	$70.560$		None	✓	✓	✓	✓	137.10.a.b	$1$	$0$	$48$	$486$	$2500$	$38910$	$-$		$\mathrm{SU}(2)$
137.12.a.a	$137$	$12$	137.a	1.a	$1$	$60$	$60$	$105.263$		None	✓	✓	✓	✓	137.12.a.a	$1$	$1$	$-96$	$-1701$	$-12500$	$-249793$	$-$		$\mathrm{SU}(2)$
137.12.a.b	$137$	$12$	137.a	1.a	$1$	$64$	$64$	$105.263$		None	✓	✓	✓	✓	137.12.a.b	$1$	$0$	$96$	$1215$	$6250$	$355259$	$+$		$\mathrm{SU}(2)$
137.14.a.a	$137$	$14$	137.a	1.a	$1$	$72$	$72$	$146.906$		None	✓	✓	✓	✓	137.14.a.a	$1$	$1$	$-192$	$-3645$	$-31250$	$-2237853$	$+$		$\mathrm{SU}(2)$
137.14.a.b	$137$	$14$	137.a	1.a	$1$	$76$	$76$	$146.906$		None	✓	✓	✓	✓	137.14.a.b	$1$	$0$	$192$	$5103$	$62500$	$1997511$	$-$		$\mathrm{SU}(2)$
137.16.a.a	$137$	$16$	137.a	1.a	$1$	$83$	$83$	$195.490$		None	✓	✓	✓	✓	137.16.a.a	$1$	$1$	$-384$	$-13122$	$-312500$	$-17750050$	$-$		$\mathrm{SU}(2)$
137.16.a.b	$137$	$16$	137.a	1.a	$1$	$87$	$87$	$195.490$		None	✓	✓	✓	✓	137.16.a.b	$1$	$0$	$384$	$13122$	$156250$	$11897498$	$+$		$\mathrm{SU}(2)$

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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.