Elliptic curves over $\Q$ of conductor 42135

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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
42135.a1	42135e4	42135.a	42135e	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{12} \cdot 5 \cdot 53^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$6360$	$48$	$0$	$1$	$9$	$3$	$0$	$1347840$	$2.508087$	$322391399464009/140831865$	$0.94878$	$5.37426$	$[1, 1, 1, -4012715, -3094399168]$	\(y^2+xy+y=x^3+x^2-4012715x-3094399168\)	2.3.0.a.1, 4.12.0-4.c.1.2, 120.24.0.?, 530.6.0.?, 1060.24.0.?, $\ldots$	$[]$
42135.a2	42135e3	42135.a	42135e	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{3} \cdot 5 \cdot 53^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$6360$	$48$	$0$	$1$	$9$	$3$	$0$	$1347840$	$2.508087$	$52183647114409/1065214935$	$0.93796$	$5.20325$	$[1, 1, 1, -2186865, 1221685512]$	\(y^2+xy+y=x^3+x^2-2186865x+1221685512\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 60.12.0.h.1, 120.24.0.?, $\ldots$	$[]$
42135.a3	42135e2	42135.a	42135e	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{6} \cdot 5^{2} \cdot 53^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3180$	$48$	$0$	$1$	$9$	$3$	$2$	$673920$	$2.161510$	$122689385209/51194025$	$0.91155$	$4.63484$	$[1, 1, 1, -290790, -31999278]$	\(y^2+xy+y=x^3+x^2-290790x-31999278\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.a.1.6, 636.24.0.?, 1060.24.0.?, $\ldots$	$[]$
42135.a4	42135e1	42135.a	42135e	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3^{3} \cdot 5^{4} \cdot 53^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$6360$	$48$	$0$	$1$	$9$	$3$	$3$	$336960$	$1.814939$	$1095912791/894375$	$0.87174$	$4.19177$	$[1, 1, 1, 60335, -3628378]$	\(y^2+xy+y=x^3+x^2+60335x-3628378\)	2.3.0.a.1, 4.12.0-4.c.1.1, 120.24.0.?, 318.6.0.?, 636.24.0.?, $\ldots$	$[]$
42135.b1	42135j1	42135.b	42135j	$1$	$1$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{5} \cdot 5^{8} \cdot 53^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12$	$2$	$0$	$0.106964391$	$1$		$10$	$43200$	$0.884651$	$185025936889/94921875$	$0.97607$	$3.18204$	$[1, 0, 0, -1675, 8750]$	\(y^2+xy=x^3-1675x+8750\)	12.2.0.a.1	$[(-25, 200)]$
42135.c1	42135k4	42135.c	42135k	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3 \cdot 5^{4} \cdot 53^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$6360$	$48$	$0$	$10.57271352$	$1$		$0$	$898560$	$2.213650$	$67563360340489/99375$	$1.01598$	$5.22751$	$[1, 0, 0, -2383495, -1416543238]$	\(y^2+xy=x^3-2383495x-1416543238\)	2.3.0.a.1, 4.12.0-4.c.1.2, 120.24.0.?, 636.24.0.?, 2120.24.0.?, $\ldots$	$[(12533206/83, 8869361756/83)]$
42135.c2	42135k2	42135.c	42135k	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 53^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3180$	$48$	$0$	$21.14542704$	$1$		$2$	$449280$	$1.867077$	$16954786009/632025$	$0.87345$	$4.44898$	$[1, 0, 0, -150340, -21714625]$	\(y^2+xy=x^3-150340x-21714625\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.b.1.6, 636.24.0.?, 1060.24.0.?, $\ldots$	$[(-1417209074/2725, 5746739751901/2725)]$
42135.c3	42135k1	42135.c	42135k	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{4} \cdot 5 \cdot 53^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$6360$	$48$	$0$	$10.57271352$	$1$		$3$	$224640$	$1.520502$	$68417929/21465$	$0.81949$	$3.93129$	$[1, 0, 0, -23935, 962432]$	\(y^2+xy=x^3-23935x+962432\)	2.3.0.a.1, 4.12.0-4.c.1.1, 120.24.0.?, 530.6.0.?, 1060.24.0.?, $\ldots$	$[(-26929/25, 21954419/25)]$
42135.c4	42135k3	42135.c	42135k	$4$	$4$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3 \cdot 5 \cdot 53^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$6360$	$48$	$0$	$42.29085408$	$1$		$0$	$898560$	$2.213650$	$1095912791/118357215$	$0.95298$	$4.68232$	$[1, 0, 0, 60335, -77712040]$	\(y^2+xy=x^3+60335x-77712040\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 30.6.0.a.1, 60.12.0.g.1, $\ldots$	$[(2314334401597834399/6861550, 3512894049475190449508376007/6861550)]$
42135.d1	42135a1	42135.d	42135a	$1$	$1$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{2} \cdot 5 \cdot 53^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$183168$	$1.745987$	$1736704/45$	$0.81978$	$4.33200$	$[0, -1, 1, -99251, -11729578]$	\(y^2+y=x^3-x^2-99251x-11729578\)	10.2.0.a.1	$[]$
42135.e1	42135b1	42135.e	42135b	$1$	$1$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{18} \cdot 5^{7} \cdot 53^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$34618752$	$4.078232$	$5705690236075638784/30267225703125$	$1.09035$	$7.03849$	$[0, -1, 1, -1475470321, 21714707659851]$	\(y^2+y=x^3-x^2-1475470321x+21714707659851\)	10.2.0.a.1	$[]$
42135.f1	42135d1	42135.f	42135d	$2$	$3$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3^{15} \cdot 5^{3} \cdot 53^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1590$	$16$	$0$	$1$	$1$		$0$	$1853280$	$2.774750$	$-13117540040704/95061508875$	$1.11332$	$5.31816$	$[0, -1, 1, -1380155, 2295397628]$	\(y^2+y=x^3-x^2-1380155x+2295397628\)	3.4.0.a.1, 30.8.0-3.a.1.2, 159.8.0.?, 1590.16.0.?	$[]$
42135.f2	42135d2	42135.f	42135d	$2$	$3$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3^{5} \cdot 5^{9} \cdot 53^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1590$	$16$	$0$	$1$	$1$		$0$	$5559840$	$3.324055$	$9220838993985536/70658419921875$	$1.04368$	$5.92441$	$[0, -1, 1, 12271585, -57895806619]$	\(y^2+y=x^3-x^2+12271585x-57895806619\)	3.4.0.a.1, 30.8.0-3.a.1.1, 159.8.0.?, 1590.16.0.?	$[]$
42135.g1	42135h1	42135.g	42135h	$1$	$1$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3^{3} \cdot 5^{5} \cdot 53^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1590$	$2$	$0$	$1.096167120$	$1$		$2$	$505440$	$2.121201$	$-1199124250624/4471875$	$1.00168$	$4.84952$	$[0, 1, 1, -621725, -189502969]$	\(y^2+y=x^3+x^2-621725x-189502969\)	1590.2.0.?	$[(1095, 21067)]$
42135.h1	42135g1	42135.h	42135g	$1$	$1$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{2} \cdot 5 \cdot 53^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1.825419575$	$1$		$2$	$3456$	$-0.239160$	$1736704/45$	$0.81978$	$2.09492$	$[0, 1, 1, -35, -91]$	\(y^2+y=x^3+x^2-35x-91\)	10.2.0.a.1	$[(7, 7)]$
42135.i1	42135i1	42135.i	42135i	$1$	$1$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{18} \cdot 5^{7} \cdot 53^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$0.168916548$	$1$		$6$	$653184$	$2.093082$	$5705690236075638784/30267225703125$	$1.09035$	$4.80142$	$[0, 1, 1, -525265, 145678306]$	\(y^2+y=x^3+x^2-525265x+145678306\)	10.2.0.a.1	$[(470, 1687)]$
42135.j1	42135c1	42135.j	42135c	$1$	$1$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{5} \cdot 5^{8} \cdot 53^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12$	$2$	$0$	$1$	$1$		$0$	$2289600$	$2.869797$	$185025936889/94921875$	$0.97607$	$5.41911$	$[1, 1, 0, -4705133, 1321494198]$	\(y^2+xy=x^3+x^2-4705133x+1321494198\)	12.2.0.a.1	$[]$
42135.k1	42135f8	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{4} \cdot 5 \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.121	2B	$25440$	$768$	$13$	$1$	$4$	$2$	$0$	$585728$	$2.276016$	$1114544804970241/405$	$1.07354$	$5.49075$	$[1, 0, 1, -6067499, -5753085163]$	\(y^2+xy+y=x^3-6067499x-5753085163\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$	$[]$
42135.k2	42135f6	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 53^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.123	2Cs	$12720$	$768$	$13$	$1$	$1$		$2$	$292864$	$1.929441$	$272223782641/164025$	$1.03897$	$4.70968$	$[1, 0, 1, -379274, -89888353]$	\(y^2+xy+y=x^3-379274x-89888353\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$	$[]$
42135.k3	42135f7	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3^{16} \cdot 5 \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.134	2B	$25440$	$768$	$13$	$1$	$1$		$0$	$585728$	$2.276016$	$-147281603041/215233605$	$1.05949$	$4.77031$	$[1, 0, 1, -309049, -124186243]$	\(y^2+xy+y=x^3-309049x-124186243\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$	$[]$
42135.k4	42135f4	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3 \cdot 5 \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$25440$	$768$	$13$	$1$	$1$		$0$	$146432$	$1.582869$	$56667352321/15$	$1.03019$	$4.56230$	$[1, 0, 1, -224779, 40999811]$	\(y^2+xy+y=x^3-224779x+40999811\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$	$[]$
42135.k5	42135f3	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{4} \cdot 5^{4} \cdot 53^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.44	2Cs	$12720$	$768$	$13$	$1$	$1$		$2$	$146432$	$1.582869$	$111284641/50625$	$1.02534$	$3.97698$	$[1, 0, 1, -28149, -843053]$	\(y^2+xy+y=x^3-28149x-843053\)	2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$	$[]$
42135.k6	42135f2	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 53^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.3	2Cs	$12720$	$768$	$13$	$1$	$1$		$2$	$73216$	$1.236296$	$13997521/225$	$0.96230$	$3.78228$	$[1, 0, 1, -14104, 634481]$	\(y^2+xy+y=x^3-14104x+634481\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$	$[]$
42135.k7	42135f1	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3 \cdot 5 \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$25440$	$768$	$13$	$1$	$1$		$1$	$36608$	$0.889721$	$-1/15$	$1.19808$	$3.19145$	$[1, 0, 1, -59, 27737]$	\(y^2+xy+y=x^3-59x+27737\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$	$[]$
42135.k8	42135f5	42135.k	42135f	$8$	$16$	\( 3 \cdot 5 \cdot 53^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 53^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.197	2B	$25440$	$768$	$13$	$1$	$1$		$0$	$292864$	$1.929441$	$4733169839/3515625$	$1.05585$	$4.32916$	$[1, 0, 1, 98256, -6303749]$	\(y^2+xy+y=x^3+98256x-6303749\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$	$[]$

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