Elliptic curves over $\Q$ of conductor 10140

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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
10140.a1	10140f1	10140.a	10140f	$1$	$1$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{7} \cdot 5 \cdot 13^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$390$	$2$	$0$	$1.364097183$	$1$		$4$	$131040$	$1.866264$	$-22478848/10935$	$1.00451$	$5.00506$	$[0, -1, 0, -82021, 12293761]$	\(y^2=x^3-x^2-82021x+12293761\)	390.2.0.?	$[(-225, 4394)]$
10140.b1	10140d1	10140.b	10140d	$1$	$1$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{13} \cdot 5^{5} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$390$	$2$	$0$	$1$	$1$		$0$	$262080$	$2.497982$	$3186827264/64769371875$	$1.15762$	$5.77648$	$[0, -1, 0, 32899, -430425399]$	\(y^2=x^3-x^2+32899x-430425399\)	390.2.0.?	$[ ]$
10140.c1	10140a1	10140.c	10140a	$1$	$1$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{15} \cdot 5^{2} \cdot 13^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$34560$	$1.646484$	$-143737544704/358722675$	$1.08334$	$4.67966$	$[0, -1, 0, -21181, 2741881]$	\(y^2=x^3-x^2-21181x+2741881\)	6.2.0.a.1	$[ ]$
10140.d1	10140e2	10140.d	10140e	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( 2^{8} \cdot 3 \cdot 5^{8} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$5.042778865$	$1$		$3$	$11520$	$0.978980$	$4877139472/1171875$	$1.11253$	$3.85374$	$[0, -1, 0, -2916, -45384]$	\(y^2=x^3-x^2-2916x-45384\)	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[(529, 12090)]$
10140.d2	10140e1	10140.d	10140e	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 5^{4} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$2.521389432$	$1$		$3$	$5760$	$0.632406$	$63404326912/5625$	$1.03071$	$3.83123$	$[0, -1, 0, -2721, -53730]$	\(y^2=x^3-x^2-2721x-53730\)	2.3.0.a.1, 12.6.0.g.1, 26.6.0.b.1, 156.12.0.?	$[(78, 450)]$
10140.e1	10140b1	10140.e	10140b	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 3^{4} \cdot 5^{2} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$16128$	$1.227318$	$8077950976/26325$	$0.94883$	$4.44207$	$[0, -1, 0, -17801, 917526]$	\(y^2=x^3-x^2-17801x+917526\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.2, 26.6.0.b.1, 52.12.0.e.1, $\ldots$	$[ ]$
10140.e2	10140b2	10140.e	10140b	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{2} \cdot 5^{4} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$32256$	$1.573893$	$-94875856/950625$	$0.90630$	$4.57605$	$[0, -1, 0, -10196, 1699320]$	\(y^2=x^3-x^2-10196x+1699320\)	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.2, 52.12.0.d.1, 312.24.0.?, $\ldots$	$[ ]$
10140.f1	10140c1	10140.f	10140c	$1$	$1$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3 \cdot 5^{2} \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$29952$	$1.220343$	$106496/75$	$0.85441$	$4.08062$	$[0, -1, 0, 5859, 78441]$	\(y^2=x^3-x^2+5859x+78441\)	6.2.0.a.1	$[ ]$
10140.g1	10140h1	10140.g	10140h	$1$	$1$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1.048012499$	$1$		$2$	$2304$	$-0.062132$	$106496/75$	$0.85441$	$2.41222$	$[0, -1, 0, 35, 25]$	\(y^2=x^3-x^2+35x+25\)	6.2.0.a.1	$[(0, 5)]$
10140.h1	10140i2	10140.h	10140i	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( 2^{8} \cdot 3 \cdot 5^{8} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$149760$	$2.261456$	$4877139472/1171875$	$1.11253$	$5.52214$	$[0, -1, 0, -492860, -101680008]$	\(y^2=x^3-x^2-492860x-101680008\)	2.3.0.a.1, 12.6.0.g.1, 52.6.0.c.1, 156.12.0.?	$[ ]$
10140.h2	10140i1	10140.h	10140i	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 5^{4} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$74880$	$1.914881$	$63404326912/5625$	$1.03071$	$5.49963$	$[0, -1, 0, -459905, -119884350]$	\(y^2=x^3-x^2-459905x-119884350\)	2.3.0.a.1, 12.6.0.g.1, 26.6.0.b.1, 156.12.0.?	$[ ]$
10140.i1	10140g1	10140.i	10140g	$1$	$1$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{15} \cdot 5^{2} \cdot 13^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$6.503762250$	$1$		$2$	$449280$	$2.928959$	$-143737544704/358722675$	$1.08334$	$6.34805$	$[0, -1, 0, -3579645, 6009594057]$	\(y^2=x^3-x^2-3579645x+6009594057\)	6.2.0.a.1	$[(-2341, 39430)]$
10140.j1	10140j1	10140.j	10140j	$1$	$1$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{7} \cdot 5 \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$390$	$2$	$0$	$1$	$1$		$0$	$10080$	$0.583789$	$-22478848/10935$	$1.00451$	$3.33666$	$[0, -1, 0, -485, 5745]$	\(y^2=x^3-x^2-485x+5745\)	390.2.0.?	$[ ]$
10140.k1	10140k2	10140.k	10140k	$2$	$3$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3 \cdot 5^{3} \cdot 13^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$390$	$16$	$0$	$1$	$1$		$0$	$36288$	$1.605474$	$-4684079104/823875$	$0.93879$	$4.71233$	$[0, 1, 0, -37405, -3192097]$	\(y^2=x^3+x^2-37405x-3192097\)	3.4.0.a.1, 30.8.0-3.a.1.1, 39.8.0-3.a.1.2, 390.16.0.?	$[ ]$
10140.k2	10140k1	10140.k	10140k	$2$	$3$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 5 \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$390$	$16$	$0$	$1$	$1$		$0$	$12096$	$1.056170$	$2809856/1755$	$0.89795$	$3.87929$	$[0, 1, 0, 3155, 20255]$	\(y^2=x^3+x^2+3155x+20255\)	3.4.0.a.1, 30.8.0-3.a.1.2, 39.8.0-3.a.1.1, 390.16.0.?	$[ ]$
10140.l1	10140l1	10140.l	10140l	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( 2^{4} \cdot 3^{8} \cdot 5^{2} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.24	2B	$520$	$48$	$0$	$1$	$1$		$1$	$32256$	$1.417593$	$3718856704/2132325$	$1.07236$	$4.35797$	$[0, 1, 0, -13745, 54900]$	\(y^2=x^3+x^2-13745x+54900\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.4, 26.6.0.b.1, 52.12.0.e.1, $\ldots$	$[ ]$
10140.l2	10140l2	10140.l	10140l	$2$	$2$	\( 2^{2} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{4} \cdot 5^{4} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.38	2B	$520$	$48$	$0$	$1$	$1$		$1$	$64512$	$1.764168$	$14647977776/8555625$	$0.99143$	$4.80716$	$[0, 1, 0, 54700, 492948]$	\(y^2=x^3+x^2+54700x+492948\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.2, 52.12.0.d.1, 104.24.0.?, $\ldots$	$[ ]$

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