Elliptic curves over $\Q$ of conductor 105222

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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
105222.a1	105222a1	105222.a	105222a	$1$	$1$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{14} \cdot 3^{15} \cdot 13 \cdot 19^{5} \cdot 71^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$105222$	$2$	$0$	$1$	$1$		$0$	$30744000$	$3.649319$	$-6422702156736768640679034611881/2708477070763914747887616$	$1.00367$	$6.13448$	$[1, 1, 0, -387255882, 2934130628052]$	\(y^2+xy=x^3+x^2-387255882x+2934130628052\)	105222.2.0.?	$[]$
105222.b1	105222b4	105222.b	105222b	$4$	$4$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2^{2} \cdot 3^{3} \cdot 13^{2} \cdot 19^{4} \cdot 71 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$32376$	$48$	$0$	$1$	$1$		$0$	$2359296$	$2.237671$	$36511337301844186615503097/168881941332$	$0.97106$	$5.08998$	$[1, 0, 1, -6911432, 6993013394]$	\(y^2+xy+y=x^3-6911432x+6993013394\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 152.12.0.?, 284.12.0.?, $\ldots$	$[]$
105222.b2	105222b2	105222.b	105222b	$4$	$4$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2^{4} \cdot 3^{6} \cdot 13^{4} \cdot 19^{2} \cdot 71^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$16188$	$48$	$0$	$1$	$1$		$2$	$1179648$	$1.891098$	$8914337209565554814137/606240323314704$	$0.97061$	$4.37069$	$[1, 0, 1, -431972, 109235090]$	\(y^2+xy+y=x^3-431972x+109235090\)	2.6.0.a.1, 12.12.0-2.a.1.1, 76.12.0.?, 228.24.0.?, 284.12.0.?, $\ldots$	$[]$
105222.b3	105222b3	105222.b	105222b	$4$	$4$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{2} \cdot 3^{12} \cdot 13^{8} \cdot 19 \cdot 71 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$32376$	$48$	$0$	$1$	$1$		$0$	$2359296$	$2.237671$	$-7346178961154982260857/2339234799533993556$	$0.97422$	$4.39187$	$[1, 0, 1, -404992, 123480530]$	\(y^2+xy+y=x^3-404992x+123480530\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 76.12.0.?, 284.12.0.?, $\ldots$	$[]$
105222.b4	105222b1	105222.b	105222b	$4$	$4$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2^{8} \cdot 3^{3} \cdot 13^{2} \cdot 19 \cdot 71^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$32376$	$48$	$0$	$1$	$1$		$1$	$589824$	$1.544523$	$2612067645573808057/563997825960192$	$0.94820$	$3.66718$	$[1, 0, 1, -28692, 1478674]$	\(y^2+xy+y=x^3-28692x+1478674\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 76.12.0.?, 114.6.0.?, $\ldots$	$[]$
105222.c1	105222c2	105222.c	105222c	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2^{3} \cdot 3^{2} \cdot 13^{8} \cdot 19^{2} \cdot 71^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$32376$	$12$	$0$	$13.85448848$	$1$		$0$	$4313088$	$2.745983$	$396465549446144137001577625/7588598278194935352$	$0.97833$	$5.29622$	$[1, 0, 1, -15304786, -23046545524]$	\(y^2+xy+y=x^3-15304786x-23046545524\)	2.3.0.a.1, 228.6.0.?, 568.6.0.?, 32376.12.0.?	$[(90956440/139, 251832633473/139)]$
105222.c2	105222c1	105222.c	105222c	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2^{6} \cdot 3 \cdot 13^{4} \cdot 19 \cdot 71^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$32376$	$12$	$0$	$6.927244242$	$1$		$1$	$2156544$	$2.399410$	$106770212554273662201625/13346836218678900288$	$0.95318$	$4.58542$	$[1, 0, 1, -988346, -334945108]$	\(y^2+xy+y=x^3-988346x-334945108\)	2.3.0.a.1, 114.6.0.?, 568.6.0.?, 32376.12.0.?	$[(-366034/25, -98005839/25)]$
105222.d1	105222g2	105222.d	105222g	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2^{13} \cdot 3^{10} \cdot 13^{2} \cdot 19^{4} \cdot 71 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$22152$	$12$	$0$	$0.372786635$	$1$		$10$	$3394560$	$2.421013$	$3225875927558062594377457/756418162059436032$	$0.99625$	$4.88015$	$[1, 1, 1, -3078279, 2077083645]$	\(y^2+xy+y=x^3+x^2-3078279x+2077083645\)	2.3.0.a.1, 156.6.0.?, 568.6.0.?, 22152.12.0.?	$[(939, 3482)]$
105222.d2	105222g1	105222.d	105222g	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{26} \cdot 3^{5} \cdot 13 \cdot 19^{2} \cdot 71^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$22152$	$12$	$0$	$0.745573271$	$1$		$9$	$1697280$	$2.074440$	$-544480505772136122097/385792173120946176$	$0.93804$	$4.19808$	$[1, 1, 1, -170119, 40208381]$	\(y^2+xy+y=x^3+x^2-170119x+40208381\)	2.3.0.a.1, 78.6.0.?, 568.6.0.?, 22152.12.0.?	$[(67, 5362)]$
105222.e1	105222h1	105222.e	105222h	$1$	$1$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{13} \cdot 3^{6} \cdot 13^{2} \cdot 19^{3} \cdot 71 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10792$	$2$	$0$	$0.158558577$	$1$		$26$	$584064$	$1.648674$	$-64024627158163005697/491499780415488$	$0.92020$	$3.94497$	$[1, 1, 1, -83344, 9287537]$	\(y^2+xy+y=x^3+x^2-83344x+9287537\)	10792.2.0.?	$[(209, 921), (285, 2821)]$
105222.f1	105222d2	105222.f	105222d	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2 \cdot 3^{6} \cdot 13^{4} \cdot 19 \cdot 71^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$10792$	$12$	$0$	$5.874466962$	$1$		$0$	$546816$	$1.570692$	$354851754919093920097/3988423179702$	$0.92789$	$4.09192$	$[1, 1, 1, -147494, 21741005]$	\(y^2+xy+y=x^3+x^2-147494x+21741005\)	2.3.0.a.1, 152.6.0.?, 284.6.0.?, 10792.12.0.?	$[(1757/4, 164369/4)]$
105222.f2	105222d1	105222.f	105222d	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{2} \cdot 3^{12} \cdot 13^{2} \cdot 19^{2} \cdot 71 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$10792$	$12$	$0$	$2.937233481$	$1$		$3$	$273408$	$1.224119$	$-80192908147326337/9208042247196$	$0.88691$	$3.38160$	$[1, 1, 1, -8984, 355061]$	\(y^2+xy+y=x^3+x^2-8984x+355061\)	2.3.0.a.1, 142.6.0.?, 152.6.0.?, 10792.12.0.?	$[(89, 475)]$
105222.g1	105222f1	105222.g	105222f	$1$	$1$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{16} \cdot 3 \cdot 13 \cdot 19^{3} \cdot 71 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$105222$	$2$	$0$	$0.176067268$	$1$		$6$	$268800$	$1.082800$	$-25662194421025681/1244697133056$	$0.87871$	$3.27437$	$[1, 1, 1, -6145, 190463]$	\(y^2+xy+y=x^3+x^2-6145x+190463\)	105222.2.0.?	$[(127, 1152)]$
105222.h1	105222e1	105222.h	105222e	$1$	$1$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2 \cdot 3^{4} \cdot 13^{11} \cdot 19^{7} \cdot 71 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$140296$	$2$	$0$	$33.44085551$	$1$		$0$	$25872000$	$3.559589$	$-53850737433335065447138796881/18425761494880921390785186$	$0.99543$	$5.76111$	$[1, 1, 1, -78672445, -338839860571]$	\(y^2+xy+y=x^3+x^2-78672445x-338839860571\)	140296.2.0.?	$[(12037961577916691/289138, 1316458988084741856289161/289138)]$
105222.i1	105222j1	105222.i	105222j	$1$	$1$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{3} \cdot 3^{6} \cdot 13^{10} \cdot 19 \cdot 71 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10792$	$2$	$0$	$0.667897645$	$1$		$2$	$1872000$	$2.231148$	$-28987906595935743520273/1084583487301083432$	$0.94675$	$4.47809$	$[1, 1, 1, -639977, 203062079]$	\(y^2+xy+y=x^3+x^2-639977x+203062079\)	10792.2.0.?	$[(981, 22324)]$
105222.j1	105222i2	105222.j	105222i	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( 2^{19} \cdot 3^{2} \cdot 13^{6} \cdot 19^{8} \cdot 71 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$22152$	$12$	$0$	$1$	$1$		$0$	$42024960$	$3.645851$	$651830049594992807318443118833/27463741155896711966097408$	$0.99877$	$5.93658$	$[1, 1, 1, -180635687, 899709589469]$	\(y^2+xy+y=x^3+x^2-180635687x+899709589469\)	2.3.0.a.1, 156.6.0.?, 568.6.0.?, 22152.12.0.?	$[]$
105222.j2	105222i1	105222.j	105222i	$2$	$2$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{38} \cdot 3 \cdot 13^{3} \cdot 19^{4} \cdot 71^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$22152$	$12$	$0$	$1$	$1$		$1$	$21012480$	$3.299278$	$18265116376750268914741007/1190206309258976028524544$	$1.00797$	$5.43782$	$[1, 1, 1, 5486553, 52257806301]$	\(y^2+xy+y=x^3+x^2+5486553x+52257806301\)	2.3.0.a.1, 78.6.0.?, 568.6.0.?, 22152.12.0.?	$[]$
105222.k1	105222l1	105222.k	105222l	$1$	$1$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{8} \cdot 3^{5} \cdot 13 \cdot 19 \cdot 71 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$105222$	$2$	$0$	$0.376899191$	$1$		$6$	$52480$	$0.418273$	$478762350767/1090941696$	$0.81893$	$2.41893$	$[1, 0, 0, 163, -1359]$	\(y^2+xy=x^3+163x-1359\)	105222.2.0.?	$[(10, 31)]$
105222.l1	105222k2	105222.l	105222k	$2$	$7$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{4} \cdot 3 \cdot 13^{7} \cdot 19 \cdot 71^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$736554$	$96$	$2$	$59.03134116$	$1$		$0$	$87588480$	$4.204720$	$-176352252185278046480312672913502369/520483235310766404806064$	$1.02478$	$7.01825$	$[1, 0, 0, -11682947706, -486046291388268]$	\(y^2+xy=x^3-11682947706x-486046291388268\)	7.48.0-7.a.2.2, 105222.2.0.?, 736554.96.2.?	$[(70033318448599980604531934/6783777665, 584322049528247216641612560504210040672/6783777665)]$
105222.l2	105222k1	105222.l	105222k	$2$	$7$	\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 71 \)	\( - 2^{28} \cdot 3^{7} \cdot 13 \cdot 19^{7} \cdot 71 \)	$1$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$736554$	$96$	$2$	$8.433048737$	$1$		$8$	$12512640$	$3.231766$	$493769165839269808367640671/484356987417093822480384$	$0.99025$	$5.31520$	$[1, 0, 0, 16466454, -21440352348]$	\(y^2+xy=x^3+16466454x-21440352348\)	7.48.0-7.a.1.2, 105222.2.0.?, 736554.96.2.?	$[(1520244, 1873679814)]$

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