LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (30 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
5544.f2	5544n2	5544.f	5544n	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{3} \cdot 7^{4} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$3584$	$0.647402$	$-138853062/290521$	$0.89988$	$3.61915$	$[0, 0, 0, -411, -6890]$	$y^2=x^3-411x-6890$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
5544.t2	5544b2	5544.t	5544b	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{9} \cdot 7^{4} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$10752$	$1.196707$	$-138853062/290521$	$0.89988$	$4.38381$	$[0, 0, 0, -3699, 186030]$	$y^2=x^3-3699x+186030$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
11088.h2	11088c2	11088.h	11088c	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{3} \cdot 7^{4} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$0.878105521$	$1$		$7$	$7168$	$0.647402$	$-138853062/290521$	$0.89988$	$3.34980$	$[0, 0, 0, -411, 6890]$	$y^2=x^3-411x+6890$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(7, 66)]$
11088.bn2	11088f2	11088.bn	11088f	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{9} \cdot 7^{4} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$21504$	$1.196707$	$-138853062/290521$	$0.89988$	$4.05755$	$[0, 0, 0, -3699, -186030]$	$y^2=x^3-3699x-186030$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
38808.m2	38808h2	38808.m	38808h	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3^{9} \cdot 7^{10} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$516096$	$2.169662$	$-138853062/290521$	$0.89988$	$4.68144$	$[0, 0, 0, -181251, -63808290]$	$y^2=x^3-181251x-63808290$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
38808.cf2	38808bv2	38808.cf	38808bv	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3^{3} \cdot 7^{10} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$172032$	$1.620356$	$-138853062/290521$	$0.89988$	$4.05761$	$[0, 0, 0, -20139, 2363270]$	$y^2=x^3-20139x+2363270$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
44352.y2	44352cw2	44352.y	44352cw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{9} \cdot 7^{4} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$4.921566275$	$1$		$15$	$172032$	$1.543282$	$-138853062/290521$	$0.89988$	$3.92053$	$[0, 0, 0, -14796, -1488240]$	$y^2=x^3-14796x-1488240$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(210, 2160), (178, 1232)]$
44352.bq2	44352m2	44352.bq	44352m	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{9} \cdot 7^{4} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$0.618556877$	$1$		$9$	$172032$	$1.543282$	$-138853062/290521$	$0.89988$	$3.92053$	$[0, 0, 0, -14796, 1488240]$	$y^2=x^3-14796x+1488240$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(-2, 1232)]$
44352.dz2	44352da2	44352.dz	44352da	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{3} \cdot 7^{4} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$2.152849736$	$1$		$5$	$57344$	$0.993975$	$-138853062/290521$	$0.89988$	$3.30448$	$[0, 0, 0, -1644, 55120]$	$y^2=x^3-1644x+55120$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(-3, 245)]$
44352.eg2	44352i2	44352.eg	44352i	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{17} \cdot 3^{3} \cdot 7^{4} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$57344$	$0.993975$	$-138853062/290521$	$0.89988$	$3.30448$	$[0, 0, 0, -1644, -55120]$	$y^2=x^3-1644x-55120$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
60984.g2	60984f2	60984.g	60984f	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{11} \cdot 3^{3} \cdot 7^{4} \cdot 11^{8} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$6.490829286$	$1$		$7$	$430080$	$1.846350$	$-138853062/290521$	$0.89988$	$4.13729$	$[0, 0, 0, -49731, 9170590]$	$y^2=x^3-49731x+9170590$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(198, 2662), (-154, 3630)]$
60984.bv2	60984bo2	60984.bv	60984bo	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{11} \cdot 3^{9} \cdot 7^{4} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$20.26646457$	$1$		$1$	$1290240$	$2.395657$	$-138853062/290521$	$0.89988$	$4.73553$	$[0, 0, 0, -447579, -247605930]$	$y^2=x^3-447579x-247605930$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(3725280238/1243, 216344280197710/1243)]$
77616.br2	77616z2	77616.br	77616z	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3^{9} \cdot 7^{10} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1.447987109$	$1$		$7$	$1032192$	$2.169662$	$-138853062/290521$	$0.89988$	$4.39325$	$[0, 0, 0, -181251, 63808290]$	$y^2=x^3-181251x+63808290$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(-203, 9604)]$
77616.ey2	77616l2	77616.ey	77616l	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{11} \cdot 3^{3} \cdot 7^{10} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$344064$	$1.620356$	$-138853062/290521$	$0.89988$	$3.80782$	$[0, 0, 0, -20139, -2363270]$	$y^2=x^3-20139x-2363270$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
121968.bn2	121968w2	121968.bn	121968w	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{11} \cdot 3^{3} \cdot 7^{4} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$0.889175764$	$1$		$9$	$860160$	$1.846350$	$-138853062/290521$	$0.89988$	$3.89242$	$[0, 0, 0, -49731, -9170590]$	$y^2=x^3-49731x-9170590$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(517, 10164)]$
121968.fa2	121968u2	121968.fa	121968u	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{11} \cdot 3^{9} \cdot 7^{4} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$2.862023520$	$1$		$5$	$2580480$	$2.395657$	$-138853062/290521$	$0.89988$	$4.45526$	$[0, 0, 0, -447579, 247605930]$	$y^2=x^3-447579x+247605930$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(-737, 13310)]$
138600.g2	138600cm2	138600.g	138600cm	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{9} \cdot 5^{6} \cdot 7^{4} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$1376256$	$2.001427$	$-138853062/290521$	$0.89988$	$4.00758$	$[0, 0, 0, -92475, 23253750]$	$y^2=x^3-92475x+23253750$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
138600.bj2	138600ev2	138600.bj	138600ev	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{3} \cdot 5^{6} \cdot 7^{4} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$458752$	$1.452120$	$-138853062/290521$	$0.89988$	$3.45082$	$[0, 0, 0, -10275, -861250]$	$y^2=x^3-10275x-861250$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
277200.hg2	277200hg2	277200.hg	277200hg	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{3} \cdot 5^{6} \cdot 7^{4} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$0.465240084$	$1$		$31$	$917504$	$1.452120$	$-138853062/290521$	$0.89988$	$3.25996$	$[0, 0, 0, -10275, 861250]$	$y^2=x^3-10275x+861250$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(45, 700), (-25, 1050)]$
277200.ll2	277200ll2	277200.ll	277200ll	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{11} \cdot 3^{9} \cdot 5^{6} \cdot 7^{4} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1.931288625$	$1$		$5$	$2752512$	$2.001427$	$-138853062/290521$	$0.89988$	$3.78593$	$[0, 0, 0, -92475, -23253750]$	$y^2=x^3-92475x-23253750$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(775, 19250)]$
310464.dm2	310464dm2	310464.dm	310464dm	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{17} \cdot 3^{3} \cdot 7^{10} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$2752512$	$1.966930$	$-138853062/290521$	$0.89988$	$3.71926$	$[0, 0, 0, -80556, 18906160]$	$y^2=x^3-80556x+18906160$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
310464.fe2	310464fe2	310464.fe	310464fe	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{17} \cdot 3^{3} \cdot 7^{10} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$2752512$	$1.966930$	$-138853062/290521$	$0.89988$	$3.71926$	$[0, 0, 0, -80556, -18906160]$	$y^2=x^3-80556x-18906160$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
310464.nw2	310464nw2	310464.nw	310464nw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{17} \cdot 3^{9} \cdot 7^{10} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$4.180457410$	$1$		$3$	$8257536$	$2.516235$	$-138853062/290521$	$0.89988$	$4.24052$	$[0, 0, 0, -725004, 510466320]$	$y^2=x^3-725004x+510466320$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(-542, 27280)]$
310464.po2	310464po2	310464.po	310464po	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{17} \cdot 3^{9} \cdot 7^{10} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$9.143737467$	$1$		$1$	$8257536$	$2.516235$	$-138853062/290521$	$0.89988$	$4.24052$	$[0, 0, 0, -725004, -510466320]$	$y^2=x^3-725004x-510466320$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(1150702/23, 1102104080/23)]$
426888.ca2	426888ca2	426888.ca	426888ca	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{11} \cdot 3^{9} \cdot 7^{10} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$61931520$	$3.368610$	$-138853062/290521$	$0.89988$	$4.92533$	$[0, 0, 0, -21931371, 84928833990]$	$y^2=x^3-21931371x+84928833990$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
426888.gs2	426888gs2	426888.gs	426888gs	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{11} \cdot 3^{3} \cdot 7^{10} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$26.42685970$	$1$		$1$	$20643840$	$2.819305$	$-138853062/290521$	$0.89988$	$4.41688$	$[0, 0, 0, -2436819, -3145512370]$	$y^2=x^3-2436819x-3145512370$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[(9549634549862/36173, 28705301577982183330/36173)]$
487872.dy2	487872dy2	487872.dy	487872dy	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{17} \cdot 3^{9} \cdot 7^{4} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$4$	$2$	$1$	$20643840$	$2.742229$	$-138853062/290521$	$0.89988$	$4.30123$	$[0, 0, 0, -1790316, -1980847440]$	$y^2=x^3-1790316x-1980847440$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
487872.ew2	487872ew2	487872.ew	487872ew	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{17} \cdot 3^{9} \cdot 7^{4} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$20643840$	$2.742229$	$-138853062/290521$	$0.89988$	$4.30123$	$[0, 0, 0, -1790316, 1980847440]$	$y^2=x^3-1790316x+1980847440$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
487872.mx2	487872mx2	487872.mx	487872mx	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{17} \cdot 3^{3} \cdot 7^{4} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$6881280$	$2.192924$	$-138853062/290521$	$0.89988$	$3.79797$	$[0, 0, 0, -198924, 73364720]$	$y^2=x^3-198924x+73364720$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$
487872.of2	487872of2	487872.of	487872of	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{17} \cdot 3^{3} \cdot 7^{4} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$264$	$12$	$0$	$1$	$1$		$1$	$6881280$	$2.192924$	$-138853062/290521$	$0.89988$	$3.79797$	$[0, 0, 0, -198924, -73364720]$	$y^2=x^3-198924x-73364720$	2.3.0.a.1, 24.6.0.b.1, 88.6.0.?, 132.6.0.?, 264.12.0.?	$[]$

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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.

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