LMFDB - Elliptic curves over $\Q$ of conductor 12870

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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

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

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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
12870.a1	12870a1	12870.a	12870a	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{7} \cdot 3^{9} \cdot 5^{5} \cdot 11 \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$17160$	$2$	$0$	$1$	$1$		$0$	$33600$	$1.151901$	$-9456845543523/57200000$	$0.90382$	$4.20344$	$[1, -1, 0, -11895, -498979]$	$y^2+xy=x^3-x^2-11895x-498979$	17160.2.0.?	$[]$
12870.b1	12870q4	12870.b	12870q	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2 \cdot 3^{10} \cdot 5 \cdot 11^{2} \cdot 13^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$0.698177919$	$1$		$18$	$65536$	$1.400196$	$30161840495801041/2799263610$	$0.94899$	$4.70661$	$[1, -1, 0, -58365, 5441395]$	$y^2+xy=x^3-x^2-58365x+5441395$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.v.1, 104.12.0.?, $\ldots$	$[(53, 1553), (183, 838)]$
12870.b2	12870q3	12870.b	12870q	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2 \cdot 3^{7} \cdot 5 \cdot 11^{8} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$2.792711677$	$1$		$12$	$65536$	$1.400196$	$1500376464746641/83599963590$	$0.93350$	$4.38948$	$[1, -1, 0, -21465, -1145345]$	$y^2+xy=x^3-x^2-21465x-1145345$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.bb.1, 52.12.0-4.c.1.1, $\ldots$	$[(-69, 95), (-79, 269)]$
12870.b3	12870q2	12870.b	12870q	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{2} \cdot 3^{8} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$1560$	$48$	$0$	$0.698177919$	$1$		$42$	$32768$	$1.053621$	$9104453457841/2226896100$	$0.90545$	$3.85003$	$[1, -1, 0, -3915, 72625]$	$y^2+xy=x^3-x^2-3915x+72625$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0.a.1, 52.12.0-2.a.1.1, 120.24.0.?, $\ldots$	$[(-4, 299), (11, 170)]$
12870.b4	12870q1	12870.b	12870q	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{4} \cdot 3^{7} \cdot 5^{4} \cdot 11^{2} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$0.698177919$	$1$		$27$	$16384$	$0.707048$	$30342134159/47190000$	$0.87423$	$3.30253$	$[1, -1, 0, 585, 6925]$	$y^2+xy=x^3-x^2+585x+6925$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.bb.1, 52.12.0-4.c.1.2, $\ldots$	$[(-7, 53), (15, 130)]$
12870.c1	12870p7	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{2} \cdot 3^{10} \cdot 5 \cdot 11^{3} \cdot 13^{12} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.1, 3.8.0.1	2B, 3B.1.1	$17160$	$384$	$5$	$1$	$1$		$4$	$1327104$	$3.027966$	$126929854754212758768001/50235797102795981820$	$1.02069$	$6.31848$	$[1, -1, 0, -9423000, 6261910740]$	$y^2+xy=x^3-x^2-9423000x+6261910740$	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 12.96.0-12.c.2.7, $\ldots$	$[]$
12870.c2	12870p6	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{4} \cdot 3^{8} \cdot 5^{2} \cdot 11^{6} \cdot 13^{6} $	$0$	$\Z/2\Z\oplus\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.6.0.1, 3.8.0.1	2Cs, 3B.1.1	$8580$	$384$	$5$	$1$	$1$		$10$	$663552$	$2.681393$	$84415028961834287121601/30783551683856400$	$1.04722$	$6.27538$	$[1, -1, 0, -8225100, 9078652800]$	$y^2+xy=x^3-x^2-8225100x+9078652800$	2.6.0.a.1, 3.8.0-3.a.1.2, 6.48.0-6.a.1.1, 12.96.0-12.a.2.13, 52.12.0-2.a.1.1, $\ldots$	$[]$
12870.c3	12870p3	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{8} \cdot 3^{7} \cdot 5 \cdot 11^{3} \cdot 13^{3} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.1, 3.8.0.1	2B, 3B.1.1	$17160$	$384$	$5$	$1$	$1$		$5$	$331776$	$2.334816$	$84392862605474684114881/11228954880$	$1.00829$	$6.27535$	$[1, -1, 0, -8224380, 9080321616]$	$y^2+xy=x^3-x^2-8224380x+9080321616$	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 12.48.0-12.g.1.12, $\ldots$	$[]$
12870.c4	12870p8	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 3^{7} \cdot 5^{4} \cdot 11^{12} \cdot 13^{3} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.1, 3.8.0.1	2B, 3B.1.1	$17160$	$384$	$5$	$1$	$1$		$4$	$1327104$	$3.027966$	$-52902632853833942200321/51713453577420277500$	$1.01622$	$6.33053$	$[1, -1, 0, -7038720, 11788581996]$	$y^2+xy=x^3-x^2-7038720x+11788581996$	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 12.96.0-12.c.4.5, $\ldots$	$[]$
12870.c5	12870p4	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{6} \cdot 3^{18} \cdot 5^{3} \cdot 11 \cdot 13^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.1, 3.8.0.2	2B, 3B.1.2	$17160$	$384$	$5$	$1$	$1$		$0$	$442368$	$2.478657$	$11621808143080380273601/1335706803288000$	$1.00205$	$6.06583$	$[1, -1, 0, -4247100, -3367494000]$	$y^2+xy=x^3-x^2-4247100x-3367494000$	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 12.96.0-12.c.1.6, $\ldots$	$[]$
12870.c6	12870p2	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{12} \cdot 5^{6} \cdot 11^{2} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.6.0.1, 3.8.0.2	2Cs, 3B.1.2	$8580$	$384$	$5$	$1$	$1$		$2$	$221184$	$2.132084$	$3590017885052913601/954068544000000$	$1.02421$	$5.21168$	$[1, -1, 0, -287100, -43470000]$	$y^2+xy=x^3-x^2-287100x-43470000$	2.6.0.a.1, 3.8.0-3.a.1.1, 6.48.0-6.a.1.2, 12.96.0-12.a.1.15, 52.12.0-2.a.1.1, $\ldots$	$[]$
12870.c7	12870p1	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{24} \cdot 3^{9} \cdot 5^{3} \cdot 11 \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.1, 3.8.0.2	2B, 3B.1.2	$17160$	$384$	$5$	$1$	$1$		$1$	$110592$	$1.785511$	$164711681450297281/8097103872000$	$0.95859$	$4.88601$	$[1, -1, 0, -102780, 12157776]$	$y^2+xy=x^3-x^2-102780x+12157776$	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 12.48.0-12.g.1.10, $\ldots$	$[]$
12870.c8	12870p5	12870.c	12870p	$8$	$12$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{6} \cdot 3^{9} \cdot 5^{12} \cdot 11^{4} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.1, 3.8.0.2	2B, 3B.1.2	$17160$	$384$	$5$	$1$	$1$		$0$	$442368$	$2.478657$	$57519563401957999679/80296734375000000$	$0.99843$	$5.54131$	$[1, -1, 0, 723780, -281835504]$	$y^2+xy=x^3-x^2+723780x-281835504$	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 12.96.0-12.c.3.3, $\ldots$	$[]$
12870.d1	12870l1	12870.d	12870l	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{5} \cdot 11^{3} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$7.479227878$	$1$		$2$	$87360$	$1.687878$	$-3158470573163361/5758438400000$	$0.98240$	$4.61855$	$[1, -1, 0, -27510, -3571084]$	$y^2+xy=x^3-x^2-27510x-3571084$	440.2.0.?	$[(6275, 493729)]$
12870.e1	12870j1	12870.e	12870j	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2 \cdot 3^{6} \cdot 5 \cdot 11 \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$1$	$1$		$0$	$6272$	$0.524659$	$-20145851361/3141710$	$0.86623$	$3.22917$	$[1, -1, 0, -510, -4870]$	$y^2+xy=x^3-x^2-510x-4870$	440.2.0.?	$[]$
12870.f1	12870k5	12870.f	12870k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{3} \cdot 3^{7} \cdot 5^{2} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.7	2B	$34320$	$192$	$1$	$2.003926709$	$1$		$2$	$491520$	$2.600266$	$23281546263261052473907201/1115400$	$1.02403$	$6.86925$	$[1, -1, 0, -53539200, 150797618136]$	$y^2+xy=x^3-x^2-53539200x+150797618136$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0.f.1, $\ldots$	$[(4245, 159)]$
12870.f2	12870k3	12870.f	12870k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 5^{4} \cdot 11^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.15	2Cs	$17160$	$192$	$1$	$1.001963354$	$1$		$10$	$245760$	$2.253693$	$5683972151443376419201/1244117160000$	$0.99969$	$5.99024$	$[1, -1, 0, -3346200, 2356839936]$	$y^2+xy=x^3-x^2-3346200x+2356839936$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.1, 12.24.0-4.b.1.1, 24.48.0-8.d.1.1, $\ldots$	$[(1047, 3)]$
12870.f3	12870k6	12870.f	12870k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{3} \cdot 3^{7} \cdot 5^{8} \cdot 11 \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.92	2B	$34320$	$192$	$1$	$2.003926709$	$1$		$2$	$491520$	$2.600266$	$-5623647484692626737921/84122230603125000$	$1.04031$	$5.99181$	$[1, -1, 0, -3334320, 2374396200]$	$y^2+xy=x^3-x^2-3334320x+2374396200$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.1, 12.12.0-4.c.1.1, 24.48.0-8.ba.1.2, $\ldots$	$[(1311, 15315)]$
12870.f4	12870k2	12870.f	12870k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{10} \cdot 5^{2} \cdot 11^{4} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.13	2Cs	$17160$	$192$	$1$	$2.003926709$	$1$		$8$	$122880$	$1.907120$	$1402524686897642881/20523074457600$	$0.96787$	$5.11236$	$[1, -1, 0, -209880, 36590400]$	$y^2+xy=x^3-x^2-209880x+36590400$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.d.2, 12.24.0-4.b.1.3, 24.48.0-8.d.2.2, $\ldots$	$[(201, 1479)]$
12870.f5	12870k1	12870.f	12870k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{24} \cdot 3^{8} \cdot 5 \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.6	2B	$34320$	$192$	$1$	$4.007853418$	$1$		$3$	$61440$	$1.560547$	$2533309721804161/1187575234560$	$0.95627$	$4.44484$	$[1, -1, 0, -25560, -679104]$	$y^2+xy=x^3-x^2-25560x-679104$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.f.2, $\ldots$	$[(-63, 855)]$
12870.f6	12870k4	12870.f	12870k	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{6} \cdot 3^{14} \cdot 5 \cdot 11^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.91	2B	$34320$	$192$	$1$	$4.007853418$	$1$		$2$	$245760$	$2.253693$	$-1769848555063681/5850659851882560$	$1.04322$	$5.32112$	$[1, -1, 0, -22680, 99377280]$	$y^2+xy=x^3-x^2-22680x+99377280$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 12.12.0-4.c.1.2, 24.48.0-8.ba.2.6, $\ldots$	$[(1161, 39879)]$
12870.g1	12870m3	12870.g	12870m	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{5} \cdot 3^{6} \cdot 5 \cdot 11^{3} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$17160$	$48$	$0$	$1$	$16$	$2$	$0$	$860160$	$2.807510$	$355995140004443961140387841/2768480$	$1.13919$	$7.15747$	$[1, -1, 0, -132887040, -589586574304]$	$y^2+xy=x^3-x^2-132887040x-589586574304$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 104.12.0.?, 312.24.0.?, $\ldots$	$[]$
12870.g2	12870m4	12870.g	12870m	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{5} \cdot 3^{6} \cdot 5^{4} \cdot 11^{12} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$17160$	$48$	$0$	$1$	$1$		$0$	$860160$	$2.807510$	$87501897507774086005761/815991377947460000$	$1.03224$	$6.27917$	$[1, -1, 0, -8324160, -9167111200]$	$y^2+xy=x^3-x^2-8324160x-9167111200$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 104.12.0.?, 312.24.0.?, $\ldots$	$[]$
12870.g3	12870m2	12870.g	12870m	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{10} \cdot 3^{6} \cdot 5^{2} \cdot 11^{6} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$17160$	$48$	$0$	$1$	$1$		$2$	$430080$	$2.460938$	$86912881496074271306241/7664481510400$	$1.08157$	$6.27846$	$[1, -1, 0, -8305440, -9210732544]$	$y^2+xy=x^3-x^2-8305440x-9210732544$	2.6.0.a.1, 12.12.0-2.a.1.1, 104.12.0.?, 220.12.0.?, 312.24.0.?, $\ldots$	$[]$
12870.g4	12870m1	12870.g	12870m	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{20} \cdot 3^{6} \cdot 5 \cdot 11^{3} \cdot 13^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$17160$	$48$	$0$	$1$	$1$		$1$	$215040$	$2.114361$	$-21075830718885163521/199306463150080$	$1.00386$	$5.40044$	$[1, -1, 0, -517920, -144501760]$	$y^2+xy=x^3-x^2-517920x-144501760$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 104.12.0.?, 110.6.0.?, $\ldots$	$[]$
12870.h1	12870c4	12870.h	12870c	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{9} \cdot 3^{9} \cdot 5^{12} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$3432$	$96$	$1$	$10.85528503$	$1$		$0$	$331776$	$2.310825$	$1900481745258486963/232375000000000$	$0.98274$	$5.49277$	$[1, -1, 0, -696750, -198629164]$	$y^2+xy=x^3-x^2-696750x-198629164$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 156.48.0.?, 264.48.0.?, $\ldots$	$[(-703991/40, 318406297/40)]$
12870.h2	12870c2	12870.h	12870c	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{3} \cdot 3^{3} \cdot 5^{4} \cdot 11^{3} \cdot 13^{6} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$3432$	$96$	$1$	$3.618428345$	$1$		$6$	$110592$	$1.761518$	$19054765821218746347/32122413895000$	$0.99002$	$5.03978$	$[1, -1, 0, -166935, 26255925]$	$y^2+xy=x^3-x^2-166935x+26255925$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 156.48.0.?, 264.48.0.?, $\ldots$	$[(-249, 7359)]$
12870.h3	12870c1	12870.h	12870c	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 11^{6} \cdot 13^{3} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$3432$	$96$	$1$	$1.809214172$	$1$		$11$	$55296$	$1.414946$	$-1538518817843307/6227391227200$	$0.97271$	$4.26351$	$[1, -1, 0, -7215, 668781]$	$y^2+xy=x^3-x^2-7215x+668781$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 78.48.0.?, 264.48.0.?, $\ldots$	$[(33, 666)]$
12870.h4	12870c3	12870.h	12870c	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{18} \cdot 3^{9} \cdot 5^{6} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$3432$	$96$	$1$	$5.427642518$	$1$		$1$	$165888$	$1.964251$	$1443395048293197/6443008000000$	$0.97378$	$4.93491$	$[1, -1, 0, 63570, -16000300]$	$y^2+xy=x^3-x^2+63570x-16000300$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 78.48.0.?, 264.48.0.?, $\ldots$	$[(12595/2, 1404905/2)]$
12870.i1	12870b2	12870.i	12870b	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2 \cdot 3^{9} \cdot 5^{4} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$1.591879844$	$1$		$6$	$12288$	$0.846608$	$149467669443/2323750$	$0.86462$	$3.76404$	$[1, -1, 0, -2985, 62675]$	$y^2+xy=x^3-x^2-2985x+62675$	2.3.0.a.1, 156.6.0.?, 264.6.0.?, 1144.6.0.?, 3432.12.0.?	$[(35, -5)]$
12870.i2	12870b1	12870.i	12870b	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 3^{9} \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$3432$	$12$	$0$	$0.795939922$	$1$		$9$	$6144$	$0.500034$	$-19683/157300$	$0.98164$	$3.09725$	$[1, -1, 0, -15, 2681]$	$y^2+xy=x^3-x^2-15x+2681$	2.3.0.a.1, 78.6.0.?, 264.6.0.?, 1144.6.0.?, 3432.12.0.?	$[(8, 51)]$
12870.j1	12870d1	12870.j	12870d	$1$	$1$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{5} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$17160$	$2$	$0$	$0.375457385$	$1$		$4$	$4800$	$0.189687$	$-27/2768480$	$1.30404$	$2.70372$	$[1, -1, 0, 0, 416]$	$y^2+xy=x^3-x^2+416$	17160.2.0.?	$[(-5, 19)]$
12870.k1	12870o3	12870.k	12870o	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{7} \cdot 3^{15} \cdot 5^{3} \cdot 11^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$64$	$2$	$0$	$37158912$	$4.684395$	$1151287518770166280399859009187288721/877598977782384000$	$1.07059$	$9.47151$	$[1, -1, 0, -196515074745, -33530596817126675]$	$y^2+xy=x^3-x^2-196515074745x-33530596817126675$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.bb.1, 52.12.0-4.c.1.1, $\ldots$	$[]$
12870.k2	12870o4	12870.k	12870o	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{7} \cdot 3^{42} \cdot 5^{3} \cdot 11^{2} \cdot 13^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$16$	$2$	$0$	$37158912$	$4.684395$	$287099942490903701230558394328721/8299347173197257908489616000$	$1.05831$	$8.59474$	$[1, -1, 0, -12369314745, -516103378502675]$	$y^2+xy=x^3-x^2-12369314745x-516103378502675$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.v.1, 104.12.0.?, $\ldots$	$[]$
12870.k3	12870o2	12870.k	12870o	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{14} \cdot 3^{24} \cdot 5^{6} \cdot 11^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$1560$	$48$	$0$	$1$	$16$	$2$	$2$	$18579456$	$4.337822$	$281076231077501634961715630808721/245403072288481536000000$	$1.05789$	$8.59250$	$[1, -1, 0, -12282194745, -523913041814675]$	$y^2+xy=x^3-x^2-12282194745x-523913041814675$	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0.a.1, 52.12.0-2.a.1.1, 120.24.0.?, $\ldots$	$[]$
12870.k4	12870o1	12870.k	12870o	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{28} \cdot 3^{15} \cdot 5^{12} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$16$	$2$	$1$	$9289728$	$3.991249$	$-67172890180943415009710808721/2029083623424000000000000$	$1.04276$	$7.71661$	$[1, -1, 0, -762194745, -8307793814675]$	$y^2+xy=x^3-x^2-762194745x-8307793814675$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.bb.1, 52.12.0-4.c.1.2, $\ldots$	$[]$
12870.l1	12870n2	12870.l	12870n	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2 \cdot 3^{6} \cdot 5^{6} \cdot 11^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$0$	$13824$	$0.727791$	$147281603041/49156250$	$0.87576$	$3.41419$	$[1, -1, 0, -990, 8050]$	$y^2+xy=x^3-x^2-990x+8050$	2.3.0.a.1, 104.6.0.?, 220.6.0.?, 5720.12.0.?	$[]$
12870.l2	12870n1	12870.l	12870n	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 3^{6} \cdot 5^{3} \cdot 11 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5720$	$12$	$0$	$1$	$1$		$1$	$6912$	$0.381217$	$881974079/929500$	$0.83354$	$2.87333$	$[1, -1, 0, 180, 796]$	$y^2+xy=x^3-x^2+180x+796$	2.3.0.a.1, 104.6.0.?, 110.6.0.?, 5720.12.0.?	$[]$
12870.m1	12870t3	12870.m	12870t	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{3} \cdot 3^{10} \cdot 5^{4} \cdot 11 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$17160$	$48$	$0$	$2.420060289$	$1$		$4$	$36864$	$1.282312$	$25176685646263969/57915000$	$0.94804$	$4.68752$	$[1, -1, 0, -54954, -4944740]$	$y^2+xy=x^3-x^2-54954x-4944740$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0-4.c.1.5, 120.24.0.?, $\ldots$	$[(-135, 70)]$
12870.m2	12870t2	12870.m	12870t	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{6} \cdot 3^{8} \cdot 5^{2} \cdot 11^{2} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$17160$	$48$	$0$	$1.210030144$	$1$		$12$	$18432$	$0.935738$	$6361447449889/294465600$	$0.89636$	$3.81214$	$[1, -1, 0, -3474, -74732]$	$y^2+xy=x^3-x^2-3474x-74732$	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 1144.12.0.?, $\ldots$	$[(-36, 70)]$
12870.m3	12870t1	12870.m	12870t	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{12} \cdot 3^{7} \cdot 5 \cdot 11 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$17160$	$48$	$0$	$2.420060289$	$1$		$5$	$9216$	$0.589165$	$31824875809/8785920$	$0.85779$	$3.25228$	$[1, -1, 0, -594, 4180]$	$y^2+xy=x^3-x^2-594x+4180$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.6, 120.24.0.?, $\ldots$	$[(29, 89)]$
12870.m4	12870t4	12870.m	12870t	$4$	$4$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{3} \cdot 3^{7} \cdot 5 \cdot 11^{4} \cdot 13^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$17160$	$48$	$0$	$2.420060289$	$1$		$4$	$36864$	$1.282312$	$1083523132511/50179392120$	$0.95398$	$4.08688$	$[1, -1, 0, 1926, -289652]$	$y^2+xy=x^3-x^2+1926x-289652$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.1, 120.24.0.?, $\ldots$	$[(99, 880)]$
12870.n1	12870w4	12870.n	12870w	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2 \cdot 3^{6} \cdot 5^{6} \cdot 11^{2} \cdot 13^{3} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$17160$	$96$	$1$	$1$	$1$		$4$	$110592$	$1.642309$	$1418098748958579169/8307406250$	$1.04337$	$5.11353$	$[1, -1, 0, -210654, 37266210]$	$y^2+xy=x^3-x^2-210654x+37266210$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 104.6.0.?, 220.6.0.?, $\ldots$	$[]$
12870.n2	12870w3	12870.n	12870w	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{2} \cdot 3^{6} \cdot 5^{3} \cdot 11 \cdot 13^{6} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$17160$	$96$	$1$	$1$	$1$		$5$	$55296$	$1.295736$	$-327495950129089/26547449500$	$1.01229$	$4.24250$	$[1, -1, 0, -12924, 607068]$	$y^2+xy=x^3-x^2-12924x+607068$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 104.6.0.?, 110.6.0.?, $\ldots$	$[]$
12870.n3	12870w2	12870.n	12870w	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{3} \cdot 3^{6} \cdot 5^{2} \cdot 11^{6} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$17160$	$96$	$1$	$1$	$1$		$0$	$36864$	$1.093002$	$7962857630209/4606058600$	$1.01501$	$3.83587$	$[1, -1, 0, -3744, 2808]$	$y^2+xy=x^3-x^2-3744x+2808$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 104.6.0.?, 220.6.0.?, $\ldots$	$[]$
12870.n4	12870w1	12870.n	12870w	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{6} \cdot 3^{6} \cdot 5 \cdot 11^{3} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$17160$	$96$	$1$	$1$	$1$		$1$	$18432$	$0.746429$	$124326214271/71980480$	$0.99017$	$3.39628$	$[1, -1, 0, 936, 0]$	$y^2+xy=x^3-x^2+936x$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 104.6.0.?, 110.6.0.?, $\ldots$	$[]$
12870.o1	12870bc4	12870.o	12870bc	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{5} \cdot 3^{16} \cdot 5^{6} \cdot 11^{3} \cdot 13^{6} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$3432$	$96$	$1$	$4.756727593$	$1$		$6$	$19353600$	$4.380424$	$4944928228995290413834018379264689/189679641808585500000$	$1.06254$	$8.89553$	$[1, -1, 0, -31943899899, 2197513725059205]$	$y^2+xy=x^3-x^2-31943899899x+2197513725059205$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 88.6.0.?, 156.48.0.?, $\ldots$	$[(108301, 2813357)]$
12870.o2	12870bc3	12870.o	12870bc	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{10} \cdot 3^{11} \cdot 5^{12} \cdot 11^{6} \cdot 13^{3} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$3432$	$96$	$1$	$2.378363796$	$1$		$13$	$9676800$	$4.033852$	$-1207087636168285491836819264689/236446260657750000000000$	$1.04813$	$8.01654$	$[1, -1, 0, -1996399899, 34339915559205]$	$y^2+xy=x^3-x^2-1996399899x+34339915559205$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 78.48.0.?, 88.6.0.?, $\ldots$	$[(25846, 64517)]$
12870.o3	12870bc2	12870.o	12870bc	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ 2^{15} \cdot 3^{36} \cdot 5^{2} \cdot 11 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$3432$	$96$	$1$	$14.27018277$	$1$		$0$	$6451200$	$3.831123$	$9532597152396244075685450929/313550122650789880627200$	$1.03874$	$7.50489$	$[1, -1, 0, -397562139, 2963216174373]$	$y^2+xy=x^3-x^2-397562139x+2963216174373$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 88.6.0.?, 156.48.0.?, $\ldots$	$[(4269223/18, 609124663/18)]$
12870.o4	12870bc1	12870.o	12870bc	$4$	$6$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 $	$ - 2^{30} \cdot 3^{21} \cdot 5^{4} \cdot 11^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$3432$	$96$	$1$	$7.135091389$	$1$		$1$	$3225600$	$3.484547$	$75991146714893572533071/15147028085515223040000$	$1.06051$	$6.88132$	$[1, -1, 0, 7941861, 159642619173]$	$y^2+xy=x^3-x^2+7941861x+159642619173$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 78.48.0.?, 88.6.0.?, $\ldots$	$[(20343/2, 4586127/2)]$

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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.

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