Elliptic curves over $\Q$ of conductor 41405

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (29 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
41405.a1	41405t1	41405.a	41405t	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{5} \cdot 7^{7} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$0.235483876$	$1$		$8$	$144000$	$0.914586$	$-1437696/21875$	$0.88927$	$3.22547$	$1$	$[0, 0, 1, -637, -32328]$	\(y^2+y=x^3-637x-32328\)	70.2.0.a.1	$[(77, 612)]$	$1$
41405.b1	41405k1	41405.b	41405k	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5 \cdot 7^{9} \cdot 13^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$1$	$1$		$0$	$1482624$	$2.418953$	$-692224/1715$	$0.81808$	$4.93237$	$1$	$[0, -1, 1, -466496, -281673078]$	\(y^2+y=x^3-x^2-466496x-281673078\)	70.2.0.a.1	$[ ]$	$1$
41405.c1	41405j1	41405.c	41405j	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{3} \cdot 7^{11} \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$1$	$1$		$0$	$1572480$	$2.575066$	$-1437696/2100875$	$1.28311$	$5.09898$	$1$	$[0, 0, 1, -107653, 683300504]$	\(y^2+y=x^3-107653x+683300504\)	70.2.0.a.1	$[ ]$	$1$
41405.d1	41405p1	41405.d	41405p	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{3} \cdot 7^{2} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.928448244$	$1$		$4$	$120960$	$1.116137$	$251559/21125$	$0.89820$	$3.45094$	$1$	$[1, -1, 1, 813, -107376]$	\(y^2+xy+y=x^3-x^2+813x-107376\)	20.2.0.a.1	$[(62, 391)]$	$1$
41405.e1	41405o1	41405.e	41405o	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{5} \cdot 7^{9} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$0.265840535$	$1$		$6$	$1347840$	$2.614761$	$-32485001809/1071875$	$0.89010$	$5.31029$	$1$	$[1, 1, 1, -3043440, 2099781172]$	\(y^2+xy+y=x^3+x^2-3043440x+2099781172\)	70.2.0.a.1	$[(8182, 720496)]$	$1$
41405.f1	41405g4	41405.f	41405g	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( 5^{3} \cdot 7^{7} \cdot 13^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3640$	$48$	$0$	$1$	$1$		$0$	$1548288$	$2.920506$	$11264882429818809/24990875$	$0.98096$	$6.02245$	$2$	$[1, -1, 1, -38673823, 92580237572]$	\(y^2+xy+y=x^3-x^2-38673823x+92580237572\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.3, 52.12.0-4.c.1.2, 56.12.0-4.c.1.5, $\ldots$	$[ ]$	$1$
41405.f2	41405g2	41405.f	41405g	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( 5^{6} \cdot 7^{8} \cdot 13^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1820$	$48$	$0$	$1$	$1$		$2$	$774144$	$2.573933$	$2844576388809/129390625$	$0.96596$	$5.24323$	$1$	$[1, -1, 1, -2444448, 1412638322]$	\(y^2+xy+y=x^3-x^2-2444448x+1412638322\)	2.6.0.a.1, 20.12.0-2.a.1.2, 28.12.0-2.a.1.1, 52.12.0-2.a.1.1, 140.24.0.?, $\ldots$	$[ ]$	$1$
41405.f3	41405g1	41405.f	41405g	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( 5^{3} \cdot 7^{10} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3640$	$48$	$0$	$1$	$1$		$1$	$387072$	$2.227360$	$13980103929/3901625$	$0.88564$	$4.74323$	$2$	$[1, -1, 1, -415603, -74099294]$	\(y^2+xy+y=x^3-x^2-415603x-74099294\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 40.12.0-4.c.1.3, 104.12.0.?, $\ldots$	$[ ]$	$1$
41405.f4	41405g3	41405.f	41405g	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{12} \cdot 7^{7} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3640$	$48$	$0$	$1$	$1$		$0$	$1548288$	$2.920506$	$451394172711/22216796875$	$1.03650$	$5.48691$	$2$	$[1, -1, 1, 1323407, 5371900356]$	\(y^2+xy+y=x^3-x^2+1323407x+5371900356\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 40.12.0-4.c.1.3, 52.12.0-4.c.1.1, $\ldots$	$[ ]$	$1$
41405.g1	41405c1	41405.g	41405c	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{3} \cdot 7^{8} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$4.932661937$	$1$		$0$	$846720$	$2.089092$	$251559/21125$	$0.89820$	$4.54918$	$1$	$[1, -1, 1, 39852, 36750172]$	\(y^2+xy+y=x^3-x^2+39852x+36750172\)	20.2.0.a.1	$[(22138/3, 3275039/3)]$	$1$
41405.h1	41405d3	41405.h	41405d	$3$	$9$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{9} \cdot 7^{7} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$8190$	$144$	$3$	$1$	$1$		$0$	$590976$	$2.382893$	$-250523582464/13671875$	$1.02112$	$5.02317$	$1$	$[0, -1, 1, -1087571, 457033527]$	\(y^2+y=x^3-x^2-1087571x+457033527\)	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.2, 70.2.0.a.1, 210.8.0.?, $\ldots$	$[ ]$	$1$
41405.h2	41405d1	41405.h	41405d	$3$	$9$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5 \cdot 7^{7} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$8190$	$144$	$3$	$1$	$1$		$0$	$65664$	$1.284279$	$-262144/35$	$0.88715$	$3.73895$	$1$	$[0, -1, 1, -11041, -491723]$	\(y^2+y=x^3-x^2-11041x-491723\)	3.4.0.a.1, 9.12.0.a.1, 63.36.0.e.1, 70.2.0.a.1, 210.8.0.?, $\ldots$	$[ ]$	$1$
41405.h3	41405d2	41405.h	41405d	$3$	$9$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{3} \cdot 7^{9} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$8190$	$144$	$3$	$1$	$1$		$0$	$196992$	$1.833586$	$71991296/42875$	$1.06493$	$4.24763$	$1$	$[0, -1, 1, 71769, 1239006]$	\(y^2+y=x^3-x^2+71769x+1239006\)	3.12.0.a.1, 63.36.0.b.1, 70.2.0.a.1, 210.24.1.?, 273.24.0.?, $\ldots$	$[ ]$	$1$
41405.i1	41405b1	41405.i	41405b	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{11} \cdot 7^{4} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$3.066930949$	$1$		$2$	$4878720$	$2.983166$	$-688691336801860161/8251953125$	$1.03647$	$6.04327$	$1$	$[1, -1, 0, -41634280, 103412470825]$	\(y^2+xy=x^3-x^2-41634280x+103412470825\)	20.2.0.a.1	$[(3936, 20509)]$	$1$
41405.j1	41405m1	41405.j	41405m	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{2} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1.276144003$	$1$		$2$	$40320$	$0.768200$	$-2401/325$	$0.91119$	$3.05934$	$1$	$[1, 0, 1, -173, 13353]$	\(y^2+xy+y=x^3-173x+13353\)	52.2.0.a.1	$[(27, 155)]$	$1$
41405.k1	41405e1	41405.k	41405e	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{5} \cdot 7^{9} \cdot 13^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$1$	$1$		$0$	$103680$	$1.332289$	$-32485001809/1071875$	$0.89010$	$3.86269$	$1$	$[1, 1, 0, -18008, 948823]$	\(y^2+xy=x^3+x^2-18008x+948823\)	70.2.0.a.1	$[ ]$	$1$
41405.l1	41405l4	41405.l	41405l	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( 5 \cdot 7^{14} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.10	2B	$7280$	$192$	$3$	$9.580475242$	$1$		$0$	$1032192$	$2.656559$	$6903498885921/374712065$	$1.05880$	$5.32663$	$2$	$[1, -1, 0, -3284969, 2182338640]$	\(y^2+xy=x^3-x^2-3284969x+2182338640\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 80.24.0.?, 112.24.0.?, $\ldots$	$[(-1550316/29, 1105270018/29)]$	$1$
41405.l2	41405l2	41405.l	41405l	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( 5^{2} \cdot 7^{10} \cdot 13^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.4	2Cs	$3640$	$192$	$3$	$19.16095048$	$1$		$2$	$516096$	$2.309986$	$40743095121/10144225$	$1.04116$	$4.84385$	$1$	$[1, -1, 0, -593644, -132739125]$	\(y^2+xy=x^3-x^2-593644x-132739125\)	2.6.0.a.1, 4.12.0.a.1, 40.24.0-4.a.1.5, 56.24.0.j.1, 104.24.0.?, $\ldots$	$[(5838513321/776, 442395678465177/776)]$	$1$
41405.l3	41405l1	41405.l	41405l	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( 5 \cdot 7^{8} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.10	2B	$7280$	$192$	$3$	$9.580475242$	$1$		$1$	$258048$	$1.963411$	$32798729601/3185$	$0.88277$	$4.82345$	$2$	$[1, -1, 0, -552239, -157805712]$	\(y^2+xy=x^3-x^2-552239x-157805712\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 80.24.0.?, 112.24.0.?, $\ldots$	$[(4694652/67, 5915352078/67)]$	$1$
41405.l4	41405l3	41405.l	41405l	$4$	$4$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{4} \cdot 7^{8} \cdot 13^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.9	2B	$7280$	$192$	$3$	$9.580475242$	$1$		$0$	$1032192$	$2.656559$	$575722725759/874680625$	$0.94006$	$5.13865$	$2$	$[1, -1, 0, 1435201, -844052182]$	\(y^2+xy=x^3-x^2+1435201x-844052182\)	2.3.0.a.1, 4.12.0.d.1, 40.24.0-4.d.1.5, 56.24.0.x.1, 104.24.0.?, $\ldots$	$[(619597/4, 486698451/4)]$	$1$
41405.m1	41405f1	41405.m	41405f	$2$	$2$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( 5 \cdot 7^{6} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$3640$	$48$	$0$	$1$	$1$		$1$	$96768$	$1.293814$	$117649/65$	$0.95681$	$3.64406$	$2$	$[1, 1, 0, -8453, -67192]$	\(y^2+xy=x^3+x^2-8453x-67192\)	2.3.0.a.1, 4.6.0.b.1, 130.6.0.?, 260.24.0.?, 280.12.0.?, $\ldots$	$[ ]$	$1$
41405.m2	41405f2	41405.m	41405f	$2$	$2$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{2} \cdot 7^{6} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$3640$	$48$	$0$	$1$	$1$		$0$	$193536$	$1.640388$	$6967871/4225$	$0.89914$	$4.02797$	$1$	$[1, 1, 0, 32952, -489523]$	\(y^2+xy=x^3+x^2+32952x-489523\)	2.3.0.a.1, 4.6.0.a.1, 260.12.0.?, 280.12.0.?, 520.24.0.?, $\ldots$	$[ ]$	$1$
41405.n1	41405a1	41405.n	41405a	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{2} \cdot 7^{8} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$6.785635500$	$1$		$0$	$282240$	$1.741154$	$-2401/325$	$0.91119$	$4.15757$	$1$	$[1, 1, 0, -8453, -4588618]$	\(y^2+xy=x^3+x^2-8453x-4588618\)	52.2.0.a.1	$[(1519/2, 53411/2)]$	$1$
41405.o1	41405n1	41405.o	41405n	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{11} \cdot 7^{10} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$53.22278335$	$1$		$0$	$34151040$	$3.956120$	$-688691336801860161/8251953125$	$1.03647$	$7.14150$	$1$	$[1, -1, 0, -2040079729, -35466397333522]$	\(y^2+xy=x^3-x^2-2040079729x-35466397333522\)	20.2.0.a.1	$[(79109483167867995998982082/29460348261, 590721868793911312518636778320997303424/29460348261)]$	$1$
41405.p1	41405i1	41405.p	41405i	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{5} \cdot 7^{7} \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$1$	$1$		$0$	$1872000$	$2.197060$	$-1437696/21875$	$0.88927$	$4.67308$	$1$	$[0, 0, 1, -107653, -71024067]$	\(y^2+y=x^3-107653x-71024067\)	70.2.0.a.1	$[ ]$	$1$
41405.q1	41405h1	41405.q	41405h	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{3} \cdot 7^{3} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$210$	$12$	$1$	$1$	$1$		$0$	$107712$	$0.865714$	$-110592/125$	$0.98030$	$3.19099$	$1$	$[0, 0, 1, -1183, 26913]$	\(y^2+y=x^3-1183x+26913\)	3.3.0.a.1, 21.6.0.a.1, 30.6.0.c.1, 70.2.0.a.1, 210.12.1.?	$[ ]$	$1$
41405.r1	41405r1	41405.r	41405r	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5 \cdot 7^{9} \cdot 13^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$2.733532327$	$1$		$0$	$114048$	$1.136480$	$-692224/1715$	$0.81808$	$3.48476$	$1$	$[0, -1, 1, -2760, -127359]$	\(y^2+y=x^3-x^2-2760x-127359\)	70.2.0.a.1	$[(1977/4, 75771/4)]$	$1$
41405.s1	41405q1	41405.s	41405q	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{3} \cdot 7^{11} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$2.014420301$	$1$		$0$	$120960$	$1.292589$	$-1437696/2100875$	$1.28311$	$3.65137$	$1$	$[0, 0, 1, -637, 311015]$	\(y^2+y=x^3-637x+311015\)	70.2.0.a.1	$[(-287/4, 35983/4)]$	$1$
41405.t1	41405s1	41405.t	41405s	$1$	$1$	\( 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 5^{3} \cdot 7^{9} \cdot 13^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$210$	$12$	$1$	$23.76757119$	$1$		$0$	$753984$	$1.838669$	$-110592/125$	$0.98030$	$4.28922$	$1$	$[0, 0, 1, -57967, -9231245]$	\(y^2+y=x^3-57967x-9231245\)	3.3.0.a.1, 21.6.0.a.1, 30.6.0.c.1, 70.2.0.a.1, 210.12.1.?	$[(1135800343993/2766, 1210465506504639367/2766)]$	$1$

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