Elliptic curves over $\Q$ of conductor 41574

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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
41574.a1	41574f1	41574.a	41574f	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{6} \cdot 3^{3} \cdot 13^{9} \cdot 41^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.6.0.1	3Ns	$6396$	$24$	$1$	$1.292510425$	$1$		$4$	$1168128$	$2.296288$	$13313738141101/119095488$	$0.94546$	$5.01206$	$[1, 1, 0, -1084814, -431969676]$	\(y^2+xy=x^3+x^2-1084814x-431969676\)	3.6.0.b.1, 39.12.0.a.1, 492.12.0.?, 6396.24.1.?	$[(5140, 357738)]$
41574.b1	41574b1	41574.b	41574b	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{3} \cdot 3^{7} \cdot 13^{6} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$984$	$2$	$0$	$1$	$1$		$0$	$148176$	$1.379427$	$-2177286259681/717336$	$0.97361$	$4.11833$	$[1, 1, 0, -45633, -3772179]$	\(y^2+xy=x^3+x^2-45633x-3772179\)	984.2.0.?	$[ ]$
41574.c1	41574c1	41574.c	41574c	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{20} \cdot 3^{7} \cdot 13^{13} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6396$	$2$	$0$	$1$	$1$		$0$	$42147840$	$4.136360$	$2974067900496992515620792961/5899782742437003264$	$1.04068$	$7.39518$	$[1, 1, 0, -5063246763, 138670602576381]$	\(y^2+xy=x^3+x^2-5063246763x+138670602576381\)	6396.2.0.?	$[ ]$
41574.d1	41574d1	41574.d	41574d	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{6} \cdot 3 \cdot 13^{9} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6396$	$2$	$0$	$1$	$1$		$0$	$193536$	$1.361155$	$30400540561/17294784$	$0.92318$	$3.71665$	$[1, 1, 0, -10988, 53136]$	\(y^2+xy=x^3+x^2-10988x+53136\)	6396.2.0.?	$[ ]$
41574.e1	41574a1	41574.e	41574a	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2 \cdot 3^{8} \cdot 13^{8} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$328$	$2$	$0$	$1$	$4$	$2$	$0$	$1687296$	$2.387215$	$-55356908515533625/538002$	$0.97992$	$5.55439$	$[1, 1, 0, -7418765, -7780690809]$	\(y^2+xy=x^3+x^2-7418765x-7780690809\)	328.2.0.?	$[ ]$
41574.f1	41574e1	41574.f	41574e	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{11} \cdot 3^{4} \cdot 13^{10} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$328$	$2$	$0$	$1$	$4$	$2$	$0$	$604032$	$2.127449$	$2056223/6801408$	$1.01702$	$4.59197$	$[1, 1, 0, 13686, 46589652]$	\(y^2+xy=x^3+x^2+13686x+46589652\)	328.2.0.?	$[ ]$
41574.g1	41574j1	41574.g	41574j	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{2} \cdot 3^{9} \cdot 13^{3} \cdot 41 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6396$	$2$	$0$	$0.148030055$	$1$		$26$	$55296$	$0.580245$	$5725732069/3228012$	$0.94872$	$2.83615$	$[1, 0, 1, -485, -700]$	\(y^2+xy+y=x^3-485x-700\)	6396.2.0.?	$[(-12, 64), (-3, 28)]$
41574.h1	41574g2	41574.h	41574g	$2$	$5$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{5} \cdot 3 \cdot 13^{6} \cdot 41^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$63960$	$48$	$1$	$1$	$25$	$5$	$0$	$3510000$	$2.977554$	$-21525971829968662032241/11122195296$	$1.06339$	$6.28226$	$[1, 0, 1, -97941419, -373084493962]$	\(y^2+xy+y=x^3-97941419x-373084493962\)	5.12.0.a.2, 65.24.0-5.a.2.1, 984.2.0.?, 4920.24.1.?, 63960.48.1.?	$[ ]$
41574.h2	41574g1	41574.h	41574g	$2$	$5$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{25} \cdot 3^{5} \cdot 13^{6} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$63960$	$48$	$1$	$1$	$1$		$0$	$702000$	$2.172836$	$-592915705201/334302806016$	$1.07782$	$4.64313$	$[1, 0, 1, -29579, -61150282]$	\(y^2+xy+y=x^3-29579x-61150282\)	5.12.0.a.1, 65.24.0-5.a.1.1, 984.2.0.?, 4920.24.1.?, 63960.48.1.?	$[ ]$
41574.i1	41574h4	41574.i	41574h	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2 \cdot 3^{8} \cdot 13^{6} \cdot 41 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$4264$	$48$	$0$	$1$	$1$		$0$	$221184$	$1.445618$	$9357915116017/538002$	$0.98265$	$4.25538$	$[1, 0, 1, -74195, -7784476]$	\(y^2+xy+y=x^3-74195x-7784476\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 104.24.0.?, 328.24.0.?, $\ldots$	$[ ]$
41574.i2	41574h2	41574.i	41574h	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{2} \cdot 3^{4} \cdot 13^{6} \cdot 41^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.4	2Cs	$4264$	$48$	$0$	$1$	$1$		$2$	$110592$	$1.099043$	$2703045457/544644$	$0.99714$	$3.48910$	$[1, 0, 1, -4905, -107144]$	\(y^2+xy+y=x^3-4905x-107144\)	2.6.0.a.1, 8.12.0.b.1, 52.12.0-2.a.1.1, 104.24.0.?, 164.12.0.?, $\ldots$	$[ ]$
41574.i3	41574h1	41574.i	41574h	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{4} \cdot 3^{2} \cdot 13^{6} \cdot 41 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$4264$	$48$	$0$	$1$	$1$		$1$	$55296$	$0.752470$	$81182737/5904$	$0.95826$	$3.15949$	$[1, 0, 1, -1525, 21296]$	\(y^2+xy+y=x^3-1525x+21296\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 52.12.0-4.c.1.2, 82.6.0.?, $\ldots$	$[ ]$
41574.i4	41574h3	41574.i	41574h	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2 \cdot 3^{2} \cdot 13^{6} \cdot 41^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.16	2B	$4264$	$48$	$0$	$1$	$4$	$2$	$0$	$221184$	$1.445618$	$25076571983/50863698$	$0.97224$	$3.78489$	$[1, 0, 1, 10305, -636452]$	\(y^2+xy+y=x^3+10305x-636452\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 52.12.0-4.c.1.1, 104.24.0.?, $\ldots$	$[ ]$
41574.j1	41574i1	41574.j	41574i	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{10} \cdot 3^{7} \cdot 13^{7} \cdot 41 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6396$	$2$	$0$	$0.279209692$	$1$		$6$	$376320$	$1.813978$	$57053285789473/1193647104$	$0.91951$	$4.42536$	$[1, 0, 1, -135542, 18845192]$	\(y^2+xy+y=x^3-135542x+18845192\)	6396.2.0.?	$[(885, 23893)]$
41574.k1	41574m1	41574.k	41574m	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{11} \cdot 3 \cdot 13^{6} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$984$	$2$	$0$	$1$	$1$		$0$	$102960$	$1.094885$	$-7916293657/251904$	$0.93151$	$3.59517$	$[1, 1, 1, -7017, -235305]$	\(y^2+xy+y=x^3+x^2-7017x-235305\)	984.2.0.?	$[ ]$
41574.l1	41574n1	41574.l	41574n	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{4} \cdot 3^{11} \cdot 13^{11} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6396$	$2$	$0$	$1$	$1$		$0$	$2365440$	$2.590649$	$82832250843593497/43147377342576$	$0.98919$	$5.10993$	$[1, 1, 1, -1534777, 230653847]$	\(y^2+xy+y=x^3+x^2-1534777x+230653847\)	6396.2.0.?	$[ ]$
41574.m1	41574l1	41574.m	41574l	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{11} \cdot 3^{4} \cdot 13^{4} \cdot 41 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$328$	$2$	$0$	$0.191970348$	$1$		$26$	$46464$	$0.844975$	$2056223/6801408$	$1.01702$	$3.14492$	$[1, 1, 1, 81, 21237]$	\(y^2+xy+y=x^3+x^2+81x+21237\)	328.2.0.?	$[(31, 218), (135, 1518)]$
41574.n1	41574k1	41574.n	41574k	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2 \cdot 3^{8} \cdot 13^{2} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$328$	$2$	$0$	$1$	$16$	$2$	$0$	$129792$	$1.104742$	$-55356908515533625/538002$	$0.97992$	$4.10734$	$[1, 1, 1, -43898, -3558391]$	\(y^2+xy+y=x^3+x^2-43898x-3558391\)	328.2.0.?	$[ ]$
41574.o1	41574o1	41574.o	41574o	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{6} \cdot 3^{4} \cdot 13^{6} \cdot 41 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$328$	$12$	$0$	$1.728380143$	$1$		$5$	$103680$	$1.140612$	$32553430057/212544$	$0.94292$	$3.72308$	$[1, 1, 1, -11242, 451511]$	\(y^2+xy+y=x^3+x^2-11242x+451511\)	2.3.0.a.1, 8.6.0.d.1, 82.6.0.?, 328.12.0.?	$[(53, 63)]$
41574.o2	41574o2	41574.o	41574o	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{3} \cdot 3^{8} \cdot 13^{6} \cdot 41^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$328$	$12$	$0$	$3.456760286$	$1$		$2$	$207360$	$1.487185$	$-2062933417/88232328$	$1.00890$	$3.86953$	$[1, 1, 1, -4482, 997719]$	\(y^2+xy+y=x^3+x^2-4482x+997719\)	2.3.0.a.1, 8.6.0.a.1, 164.6.0.?, 328.12.0.?	$[(391, 7499)]$
41574.p1	41574p1	41574.p	41574p	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{6} \cdot 3^{3} \cdot 13^{3} \cdot 41^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.6.0.1	3Ns	$6396$	$24$	$1$	$1.554923123$	$1$		$2$	$89856$	$1.013813$	$13313738141101/119095488$	$0.94546$	$3.56501$	$[1, 1, 1, -6419, -199087]$	\(y^2+xy+y=x^3+x^2-6419x-199087\)	3.6.0.b.1, 39.12.0.a.1, 492.12.0.?, 6396.24.1.?	$[(-47, 62)]$
41574.q1	41574t1	41574.q	41574t	$2$	$3$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2 \cdot 3^{3} \cdot 13^{6} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$12792$	$16$	$0$	$1$	$1$		$0$	$46800$	$0.608270$	$-389017/2214$	$0.87552$	$2.88135$	$[1, 0, 0, -257, 5199]$	\(y^2+xy=x^3-257x+5199\)	3.4.0.a.1, 39.8.0-3.a.1.1, 984.8.0.?, 12792.16.0.?	$[ ]$
41574.q2	41574t2	41574.q	41574t	$2$	$3$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{3} \cdot 3 \cdot 13^{6} \cdot 41^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$12792$	$16$	$0$	$1$	$1$		$0$	$140400$	$1.157576$	$270840023/1654104$	$0.95436$	$3.48499$	$[1, 0, 0, 2278, -129156]$	\(y^2+xy=x^3+2278x-129156\)	3.4.0.a.1, 39.8.0-3.a.1.2, 984.8.0.?, 12792.16.0.?	$[ ]$
41574.r1	41574q1	41574.r	41574q	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{4} \cdot 3^{3} \cdot 13^{7} \cdot 41 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6396$	$2$	$0$	$0.294078707$	$1$		$4$	$64512$	$1.066767$	$4165509529/230256$	$0.83653$	$3.52976$	$[1, 0, 0, -5665, 155609]$	\(y^2+xy=x^3-5665x+155609\)	6396.2.0.?	$[(-64, 539)]$
41574.s1	41574r1	41574.s	41574r	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{14} \cdot 3^{12} \cdot 13^{6} \cdot 41 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$328$	$12$	$0$	$1$	$1$		$1$	$3628800$	$2.996853$	$10341755683137709164937/356992303104$	$1.06164$	$6.21333$	$[1, 0, 0, -76708512, -258597411840]$	\(y^2+xy=x^3-76708512x-258597411840\)	2.3.0.a.1, 8.6.0.d.1, 82.6.0.?, 328.12.0.?	$[ ]$
41574.s2	41574r2	41574.s	41574r	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{7} \cdot 3^{24} \cdot 13^{6} \cdot 41^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$328$	$12$	$0$	$1$	$1$		$0$	$7257600$	$3.343430$	$-10298071306410575356297/60769798505543808$	$1.06173$	$6.21388$	$[1, 0, 0, -76600352, -259362989952]$	\(y^2+xy=x^3-76600352x-259362989952\)	2.3.0.a.1, 8.6.0.a.1, 164.6.0.?, 328.12.0.?	$[ ]$
41574.t1	41574s2	41574.t	41574s	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{5} \cdot 3^{6} \cdot 13^{12} \cdot 41 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12792$	$12$	$0$	$1$	$1$		$0$	$1451520$	$2.426254$	$21151205362964377/4616591814432$	$0.95995$	$4.98157$	$[1, 0, 0, -973697, -291938583]$	\(y^2+xy=x^3-973697x-291938583\)	2.3.0.a.1, 156.6.0.?, 328.6.0.?, 12792.12.0.?	$[ ]$
41574.t2	41574s1	41574.t	41574s	$2$	$2$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( - 2^{10} \cdot 3^{3} \cdot 13^{9} \cdot 41^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12792$	$12$	$0$	$1$	$1$		$1$	$725760$	$2.079681$	$56300788871783/102108404736$	$0.94172$	$4.49538$	$[1, 0, 0, 134943, -27860535]$	\(y^2+xy=x^3+134943x-27860535\)	2.3.0.a.1, 78.6.0.?, 328.6.0.?, 12792.12.0.?	$[ ]$
41574.u1	41574u1	41574.u	41574u	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 41 \)	\( 2^{2} \cdot 3^{9} \cdot 13^{9} \cdot 41 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6396$	$2$	$0$	$1$	$1$		$0$	$718848$	$1.862719$	$5725732069/3228012$	$0.94872$	$4.28320$	$[1, 0, 0, -81884, -1455468]$	\(y^2+xy=x^3-81884x-1455468\)	6396.2.0.?	$[ ]$

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