Elliptic curves over $\Q$ of conductor 10470

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

Results (9 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
10470.a1	10470a4	10470.a	10470a	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 349^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$8376$	$48$	$0$	$4.183959109$	$1$		$4$	$124416$	$1.798128$	$1397790417785316543001/640892891563200$	$0.97710$	$5.26013$	$1$	$[1, 1, 0, -232937, 43157829]$	\(y^2+xy=x^3+x^2-232937x+43157829\)	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 2792.24.0.?, 8376.48.0.?	$[(313, 861)]$	$1$
10470.a2	10470a3	10470.a	10470a	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( 2^{6} \cdot 3^{12} \cdot 5^{8} \cdot 349 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$8376$	$48$	$0$	$1.045989777$	$1$		$6$	$124416$	$1.798128$	$235301185027835613721/4636822725000000$	$0.97060$	$5.06764$	$2$	$[1, 1, 0, -128617, -17502779]$	\(y^2+xy=x^3+x^2-128617x-17502779\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 698.6.0.?, 1396.24.0.?, $\ldots$	$[(-198, 599)]$	$1$
10470.a3	10470a2	10470.a	10470a	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( 2^{12} \cdot 3^{6} \cdot 5^{4} \cdot 349^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$4188$	$48$	$0$	$2.091979554$	$1$		$8$	$62208$	$1.451553$	$537369779909439001/227309898240000$	$0.95787$	$4.41057$	$1$	$[1, 1, 0, -16937, 433029]$	\(y^2+xy=x^3+x^2-16937x+433029\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 1396.24.0.?, 4188.48.0.?	$[(-7, 746)]$	$1$
10470.a4	10470a1	10470.a	10470a	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( - 2^{24} \cdot 3^{3} \cdot 5^{2} \cdot 349 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$8376$	$48$	$0$	$4.183959109$	$1$		$3$	$31104$	$1.104980$	$4916382075769319/3952292659200$	$0.93742$	$3.90345$	$2$	$[1, 1, 0, 3543, 52101]$	\(y^2+xy=x^3+x^2+3543x+52101\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[(107, 1239)]$	$1$
10470.b1	10470b1	10470.b	10470b	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( - 2^{8} \cdot 3^{9} \cdot 5^{5} \cdot 349 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10470$	$2$	$0$	$0.130578303$	$1$		$10$	$23040$	$1.124908$	$264596923272599/5495493600000$	$0.95047$	$3.97151$	$1$	$[1, 0, 1, 1337, -111094]$	\(y^2+xy+y=x^3+1337x-111094\)	10470.2.0.?	$[(55, 332)]$	$1$
10470.c1	10470c1	10470.c	10470c	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( - 2 \cdot 3^{5} \cdot 5^{3} \cdot 349 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$41880$	$2$	$0$	$1$	$1$		$0$	$4680$	$0.086005$	$881974079/21201750$	$0.86036$	$2.62524$	$1$	$[1, 1, 1, 20, 227]$	\(y^2+xy+y=x^3+x^2+20x+227\)	41880.2.0.?	$[ ]$	$1$
10470.d1	10470d1	10470.d	10470d	$2$	$7$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{7} \cdot 349 \)	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$293160$	$96$	$2$	$1$	$1$		$6$	$38808$	$1.406019$	$-10372797669976737841/7632630000000$	$0.95720$	$4.73052$	$1$	$[1, 0, 0, -45435, 3726225]$	\(y^2+xy=x^3-45435x+3726225\)	7.48.0-7.a.1.2, 41880.2.0.?, 293160.96.2.?	$[ ]$	$1$
10470.d2	10470d2	10470.d	10470d	$2$	$7$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( - 2 \cdot 3 \cdot 5 \cdot 349^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$293160$	$96$	$2$	$1$	$49$	$7$	$0$	$271656$	$2.378975$	$671282315177095816559/18919046447754148470$	$1.10931$	$5.59844$	$1$	$[1, 0, 0, 182415, -207095505]$	\(y^2+xy=x^3+182415x-207095505\)	7.48.0-7.a.2.2, 41880.2.0.?, 293160.96.2.?	$[ ]$	$1$
10470.e1	10470e1	10470.e	10470e	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 349 \)	\( - 2^{4} \cdot 3 \cdot 5 \cdot 349 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10470$	$2$	$0$	$1$	$1$		$0$	$1152$	$-0.371619$	$-13997521/83760$	$0.78085$	$2.04000$	$1$	$[1, 0, 0, -5, -15]$	\(y^2+xy=x^3-5x-15\)	10470.2.0.?	$[ ]$	$1$

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